; TeX output 1997.01.06:1824*tj??ÉZ"jDtGGcmr17X>Y-pic7tUser'sGuide|XQ cmr12Kristo erH.Rose !", cmsy10hkrisrose@brics.dki2 K cmsy8YVVersion3.3,DecemrbSer19,1996'ExXtypGesettingsystem.EXY-picworkswithmostofthemanyformatsavqailable,$': cmti10e.g.,plainTU>'ExX,L5ffٓRcmr7A͉TU>'EX,andB !", cmsy10AU>'M S-TU>'EX.JSeveralstylesofinputforvqariousOdiagramtypGesaresupported;theyallshareamnemonicdnotationbasedonthelo}'gical'fcompositionofvisualc}'omponents.This[guideconcentratesonhowtotypGeset)Y\matrix-like"diagrams,^Zsuchascommutativediagrams,UUinthefollowingstyle:; &ps: SDict begin xyc end q b> cmmi10UC" {mark 51.83813 -75.1666 16.03137 -44.38164 0.0 0.0 1.0 0.073 q}xy+p 0ercmmi7y3Bu" {2104 10 /xy AB}xyG" {mark 51.83813 -75.1666 16.03137 -44.38164 0.0 0.0 0.073 0.89929 q}xyE" {mark 51.83813 -75.1666 16.03137 -44.38164 0.0 0.0 1.0 0.89929 q}xyD" {mark 104.25197 -37.5833 56.3374 -7.55629 0.0 0.0 1.0 0.06201 q}xy<PxgC " {2476 10 /xy AB}xyH" {mark 104.25197 -37.5833 56.3374 -7.55629 0.0 0.0 0.06201 0.92188 q}xyD" {mark 104.25197 -37.5833 56.3374 -7.55629 0.0 0.0 1.0 0.92194 q}xy ?" {0.03091 -0.07153 dt}xyџ(x;y@L)ܟ ۰" {12.6947 -9.19044 dt}xy0  q" {2330 10 /xy AB}xy0  q" {12.7148 -9.19044 dt}xy0  q" {0.05101 -0.05086 dt}xy(%ŵX¸Z;YǍ:," {0.0 0.0 l}xy=6Rq:Ba" {1024 10 /xy AB}xyǍ:D" {0.0 -24.0 l}xyǍ:D" {0.0 0.0 l}xyO #7" {0.0 0.0 l}xyRa):pg #7" {3072 10 /xy AB}xyg #7" {24.0 0.0 l}xyg #7" {0.0 0.0 l}xyj &ĵXǍo6+" {0.0 0.0 l}xyg7ôfo6Ba" {1024 10 /xy AB}xyǍo6D" {0.0 -24.74998 l}xyǍo6D" {0.0 0.0 l}xy6ȄL7YAϡHm" {0.0 0.0 l}xyR퇟DoghpHm" {3072 10 /xy AB}xyhpHm" {38.6291 0.0 l}xyhpHm" {0.0 0.0 l}xykpL7Z`wasUUtypGesetbytheUQXY U-picinputlinesN8%}[dr]|-{(x,y)}>\\ &?X\times_ZY\ar[d]^q\ar[r]_pY?&?X\ar[d]_f$\\ &?Y\ar[r]^g&ZS}SuchUUdiagramshavethefollowingcharacteristics:d SpGeci edTasamatrixofentriesthatareautomat-icallyUUalignedinrowsandcolumns.β Any?entrymaybGeconnectedtoanyotherentryusing?avqarietyofarrowstylesallrotatedandstretchedUUasrequired. ArrowsmaybGedecoratedwithlabelsthataretiedto8aspGeci edpointalongthearrowandextendinayparticulardirection; andarrowsmaybGepaired,cross,andܔvisit/bGendaroundotherentries\ontheway*."eSeveral8otherstylesofinputaresuppGorted;ashortsurveyTofthepGossibilitiesisincludedlastattheendalongqwithinformationonhowqXY -piccanbGeobtained.&߉ff^ A ß-:!q% cmsy6L|{Ycmr8BRICS,+ComputerScience, _AarhÎusUniversity(bld.540), NyXMunkÎegade,DK{8000AarhusC,Denmark.Z:ContentsNˍ:&"V cmbx10Preface2:1;Basics62 by;1.1 ?Loading8..................2;1.2 ?Entries|...................2;1.3 ?Arrowsҍ...................2;1.4 ?LabGels...................3;1.5 ?BreaksU ...................3;1.6 ?Curvingx..................3;1.7 ?SpGeedingUUuptypesetting* .........4Nˍ:2;MoreTArro9wsandLabQelsZ4;2.1 ?ExplicitUUlabGelpositioning⍍........4;2.2 ?LabGelingUUwithanyob8ject1&.........5;2.3 ?MoreUUarrowstylesL.............5;2.4 ?SlidingUUarrowssideways.........6;2.5 ?MoreUUtargets*?...............6;2.6 ?ChangingUUthetarget⍍...........6;2.7 ?ArrowsUUpassingunderM..........7;2.8 ?MoreUUbGendingarrowsǍ...........7;2.9 ?De ningUUnewarrowtypGes........8:3;MoreTEn9tries8;3.1 ?ManualUUentryformatting΍.........8;3.2 ?ExtraUUentriesoutsidethematrix7....9;3.3 ?SpacingUUandrotation...........9;3.4 ?EntryUUstyleƸ................9;3.5 ?NamingUUforlateruseastargets.....10;3.6 ?GroupingUUob8jects;􍍑.............10:4;Av\railabilit9yTandF urtherInformation11;4.1 ?GettingUQXY U-pic#...............11;4.2 ?BackwardsUUcompatibilityz.........11;4.3 ?F*urtherUUreadingTߍ..............11;4.4 ?Credits?...................12:A;Answ9ersTtoallexercisesZ12:ReferencesZ14:Indexޕ14LWj:1**tj??gwPrefaceyThis#guideexplainssomefeaturesofXY+#-picthatare relevqant totypGesettingof\matrix-likediagrams"asused in,6 forexample,categorytheory;bpleaserefertothe7dreferencemanual[8]forcompleteinformationonthe#describGedconstructions.1TheguideassumesthatyouhavesomeexpGerienceinusingTU>'ExXfortypGeset-ting}mathematics,e.g.,havestudied[2,ch.16{19],[3,sec.v3.3],or[9],andthatrXY v-picisinstalledonyourTU>'ExXsystemdasdescribGedintheINSTALL+! leaccompanyingtheUUdistribution. M Thepy rstsectiondescribGeswhatyouneedtogetstarted,qinparticularallthatisneededtotypGesetthediagramintheabstract.4Section2and3explainad-vqanceduseofarrowsandentries,&respGectively*.^FFinally,section˶4explainswhereandunderwhatconditionsXY-picisavqailable,givestherelationofversion3.3topreviousG>versions,Jandlistsfurthersourcesofinforma-tion. Throughout@xwegiveexercisesthatyoushouldbGeabletosolveasyougoalong;YallexercisesareansweredattheUUendjustpriortothereferencesandindex.!e1]BasicsyThis.sectionexplainsthe*XY d.-diagramconstructioncon-ceptsKneededtogetstartedwithtypGesettingmatrix-likediagrams.y׍'N cmbx121.1LoadingThebXY {f-picfsetupusedinthisguideisloadedbyinsert-ingUUthelines ȉff2 }Q\input?xyQ\xyoption{all}Off2Rtinhthede nitionspartofyourdoGcument.^1 &Ifyouwishto|loadonlythefeaturesyouuse, oryouwishtousenon-standardUfacilitieslikethev2+backwardscompati-bility>moGde^2 ortheps(- cmcsc10PostScript^3backend>thenthisisalsopGossibleasdescribedinthereferencemanual[8].1.2EntriesAUUdiagramiscreatedbythecommand ȉff2 }O\xymatrix{R...}Off2 bwherethe\..."shouldbGereplacedbyentries0tobealigne}'dinrowsandcolumns'vwherecff^ J= "5-:Aacmr61LL#A TAEMXFd22cmmi8"B([3@]XuserscanuseCscmtt8\usepackage[all]{xy}&@$. > "5-:2LIf,yÎouusetheversion2loadingcommand\inputxypic3Ȅthen theXv2optionwillb}"ŸN8ps: SDict begin xyc endΞ" {0.02267 -0.0082 dt}xy " {1498 10 /xy AB}xy " {10.00002 -21.60002 dt}xy " {0.02267 -0.0082 dt}xy@{.>}F]N8ps: SDict begin xyc endY핞" {0.02267 -0.0082 dt}xyl" {0.02267 -0.0082 dt}xy " {1498 /XT tt}xyY V'" {8.95448 -19.33653 dt}xyl V'" {8.95448 -19.33653 dt}xy:]@{:>}jN8ps: SDict begin xyc end " {1498 10 /xy AB}xy#  " {1498 g}xyw " {1498 g}xy " {1498 g}xy^@{~>}ݘN8ps: SDict begin xyc endΞ" {0.02267 -0.0082 dd}xy " {1498 10 /xy AB}xy " {10.00002 -21.60002 dd}xy " {0.02267 -0.0082 dd}xyݘ@{-->}]N8ps: SDict begin xyc endΞ" {0.02267 -0.0082 l}xy " {10.00002 -21.60002 l}xy " {0.02267 -0.0082 l}xy]@{-}]|N8ps: SDict begin xyc end]|@{}%Yǟ ExerciseT2: TypGesetO}ps: SDict begin xyc endڪǍ8" {0.0 0.0 dd}xyǍ8" {0.0 -24.0 dd}xyǍ8" {0.0 0.0 dd}xy Q'" {0.0174 -0.01903 l}xy #h" {0.0174 -0.01903 l}xy#Q"" {24.3924 -24.0 l}xy"#" {24.3924 -24.0 l}xy#Q"" {0.0174 -0.01903 l}xy"#" {0.0174 -0.01903 l}xy " {0.0 0.0 l}xy#" {23.99998 0.0 l}xy#" {0.0 0.0 l}xy&ڪǍ(8" {0.0 0.0 dt}xyǍ(8" {0.0 -24.0 dt}xyǍ(8" {0.0 0.0 dt}xy"Lp&"Lp# " {0.0 0.0 l}xy  " {-1024 10 /xy AB}xy  " {-23.99998 0.0 l}xy  " {0.0 0.0 l}xy.z 1.4Lab`elsuTY*ouscanputlabGelsonarrows.̂Labelsareconceptu- alizedassub-andsupGerscriptsonarrowssuchthattheyareplacedintheusualpGositions(as\limits"),i.e.,^?reads\abGove"?and_\below"onanarrowpGointingright.GNotice}thatthepGositionsdependonly_onthedirection`!ofthearrow,theabsolutenotionsof\up,"\down,"UUetc.qarenotimpGortant.qF*orexample,N8$\xymatrix@1{QX\ar[r]^a_b?&Y&Z\ar[l]^A_B}$hwillc%setps: SDict begin xyc end!ǵXƟ" {0.0 0.0 l}xyǴa ~8b%Ɵ" {3072 10 /xy AB}xy%Ɵ" {22.0 0.0 l}xy%Ɵ" {0.0 0.0 l}xy&ƞ!ǵYH!ZE" {0.0 0.0 l}xy7jPA7B/" {-1024 10 /xy AB}xy/" {-21.99998 0.0 l}xy/" {0.0 0.0 l}xyU(the@1isaspGecialcodethatocanbGeusedfor\one-line"diagramstoimprovetheplacementNontheline;KmoresuchspacingcoGdesaredescribGedUUinsection3.3). It`ispGossibletouselabelsthatarenotsingleletters,digits,orcontrolsequences:2ifasimplemathformulainthedefaultstyle(scriptstyle)isdesiredthensimplyenclosein{...}꧲.InpracticeanythingcanbGeusedasaUUlabGelasdescribedinsection2.2. Each/labGelisplacedperpendiculartothearrowatthe^qpGointhalfwaybGetweenthecentersofthebaseandtarget~ob8jects. BThisisusuallythemoststhethic,however,Bin"diagramswherethesizesoftheentriesvqaryu[muchitissometimesnicertoplacethelabGelatVthecenteroftheactualarrow.vThisbGehaviourisrequestedbyinsertinga-(minus)rightafterthe^卑orUU_R:ps: SDict begin xyc end!ǵA8BQCDJ4" {0.0 0.0 l}xyRlq+`4" {3072 10 /xy AB}xy`4" {22.0 0.0 l}xy`4" {0.0 0.0 l}xya4!ǵBp²wasUUtypGesetbyƍ$\xymatrix@1{QA\times?B\timesC\timesD\ar[r]^-{+}&B}$r(itbGecomesps: SDict begin xyc end!ǵA8BQCDJ4" {0.0 0.0 l}xyBtq+`4" {3072 10 /xy AB}xy`4" {22.0 0.0 l}xy`4" {0.0 0.0 l}xya4!ǵBlmwithoutthe-).9In fact-ɲisinjustoneofthemaypGossibleplacingsoflabGelsUUdescribedinsection2.1.gw:Exercise3: TypGesetibthesecondaxiomofcategory :theoryUUas0Dmps: SDict begin xyc end qA " {0.0 0.0 l}xyMEVf%" {3072 10 /xy AB}xy%" {23.99998 0.0 l}xy%" {0.0 0.0 l}xy Z" {0.02487 -0.02586 l}xy lf;g% q" {2074 10 /xy AB}xy% q" {24.63425 -24.0 l}xy% q" {0.02487 -0.02586 l}xy( qBǍ,j" {0.0 0.0 l}xy/g, q" {1024 10 /xy AB}xyǍ,j" {0.0 -24.0 l}xyǍ,j" {0.0 0.0 l}xy3B" {0.04977 -0.02951 l}xyB^ҟ g@L;hL2 q" {2088 10 /xy AB}xyL2 q" {24.98727 -24.0 l}xyL2 q" {0.04977 -0.02951 l}xy(%ŵC3y"w" {0.0 0.0 l}xy=] *ShK8"w" {3072 10 /xy AB}xyK8"w" {24.11215 0.0 l}xyK8"w" {0.0 0.0 l}xyN8%ŵD4i :1.5:Breaks덒:It isalsopGossibleto\break"anarrowwithalabel:usinghthe|character:$\xymatrix@1{A\ar[r]|f&B}$ :willUUsetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xyMaǴfM" {7.80464 0.0 l}xy#" {3072 10 /xy AB}xy#" {9.51126 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB/9. ؍;IfTyoujustwantanemptybreakyoushouldusethe P:spGecialG\holebreak:jthearrowps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy" {7.14668 0.0 l}xy#" {3072 10 /xy AB}xy#" {8.8533 0.0 l}xy#" {0.0 0.0 l}xy$!B2߲wasGtypeset :byincluding$\xymatrix@1{?A\ar[r]|\hole&B}$:inUUthetext. 2J;Aodi erentoWuseofbreaksistoplacealabGelsome-:whereinadiagramoutsidethenormalmatrixmesh::thisisaccomplishedby\breaking"aninvisiblearrow:obtainedUUusingthe@{}arrowstyle:qthesquaredC@ps: SDict begin xyc endK qApd=Ǎ j" {0.0 0.0 l}xy  q" {1024 10 /xy AB}xyǍ j" {0.0 -24.0 l}xyǍ j" {0.0 0.0 l}xy " {0.0 0.0 l}xy&8" {3072 10 /xy AB}xy&8" {24.29338 0.0 l}xy&8" {0.0 0.0 l}xy)8 qBǍ-!Tj" {0.0 0.0 l}xy-!T q" {1024 10 /xy AB}xyǍ-!Tj" {0.0 -24.0 l}xyǍ-!Tj" {0.0 0.0 l}xy%B9"w" {0.0 0.0 l}xy&2"w" {3072 10 /xy AB}xy&2"w" {24.11214 0.0 l}xy&2"w" {0.0 0.0 l}xy)2%C;8 :wasUUtypGesetbyN8:\xymatrix{\ar?@{}[dr]|{=}*7A?\ar[d]\ar[r]&B\ar[d]\\*7B?\ar[r])&C}:ThereUUismoreonbreaksinsection2.7. :Exercisew?4: TypGesetthe rstaxiomofcategorythe-:oryUUasthedisplayv?ps: SDict begin xyc end  qAǍ j" {0.0 0.0 l}xyqf  q" {1024 10 /xy AB}xyǍ j" {0.0 -24.0 l}xyǍ j" {0.0 0.0 l}xyo!" {0.0 0.0 l}xybEVf)<" {3072 10 /xy AB}xy)<" {24.29338 0.0 l}xy)<" {0.0 0.0 l}xy,< qB*"" {0.0 -0.0101 l}xyZܞimO \cmmi5B 2 :" {-9.48961 -9.18126 l}xyQ q" {-34 10 /xy AB}xyQ q" {-9.4896 -9.18124 l}xyQ q" {0.0 -0.0101 l}xyǍ0Xj" {0.0 0.0 l}xy3Xg0X q" {1024 10 /xy AB}xyǍ0Xj" {0.0 -24.0 l}xyǍ0Xj" {0.0 0.0 l}xy%ŵB="w" {0.0 0.0 l}xy(zg)"w" {3072 10 /xy AB}xy)"w" {24.11214 0.0 l}xy)"w" {0.0 0.0 l}xy,%ŵC8;:1.6:Curving덒:ArrowscanbGemadetocurve,forexampletoavoid:goingthroughanotherentry*,U>usingthespGecialstyle:@/j4curving}/"z.]Thesimpleststylesofcurving^arethefol-:lowing,UUshownappliedtoanarrowfromAtoBq:d"ps: SDict begin xyc end @/^/D qA@" {mark 89.41823 0.0 70.52153 12.0 51.62483 0.0 1.0 0.17871 q}xyg@{" {2664 10 /xy AB}xyD" {mark 89.41823 0.0 70.52153 12.0 51.62483 0.0 0.17871 0.81372 q}xy@" {mark 89.41823 0.0 70.52153 12.0 51.62483 0.0 1.0 0.81366 q}xyj? qB r@/_/DAN" {mark 89.41823 -20.0334 70.52153 -32.0334 51.62483 -20.0334 1.0 0.17871 q}xyg@M" {3480 10 /xy AB}xyR" {mark 89.41823 -20.0334 70.52153 -32.0334 51.62483 -20.0334 0.17871 0.81372 q}xyN" {mark 89.41823 -20.0334 70.52153 -32.0334 51.62483 -20.0334 1.0 0.81366 q}xyj?B(S@/_1pc/D)AN" {mark 89.41823 -40.0668 70.52153 -64.0668 51.62483 -40.0668 1.0 0.15894 q}xyhIJ,z" {3955 10 /xy AB}xyR" {mark 89.41823 -40.0668 70.52153 -64.0668 51.62483 -40.0668 0.15894 0.84106 q}xyN" {mark 89.41823 -40.0668 70.52153 -64.0668 51.62483 -40.0668 1.0 0.84106 q}xyj?)BLWj:3yՠ*tj??gwAsthelastexampleshowsadimensioncanbGeinserted justUUafter^ ꧲or_ifmoreorlesscurvingisdesired. In wcaseitiseasiertospGecifythein-andout-goingdirectionsofthecurvingthenthatisalsopGossible:@useff2 {_r@(inc,`out)&ff2 ;whereUUinandoutH-areoneofthefollowingdir}'ections!:45L̚ps: SDict begin xyc endn)" {12.0 12.0 12.0 12.0 ox}xy N$dlǍ9f{" {-10.91502 -10.91502 l}xy9B" {0 10 /xy AB}xy'$dǍ)" {0.0 -17.94443 l}xy)" {1024 10 /xy AB}xy=Զ$dr=B" {10.92094 -10.91502 l}xy=B" {2048 10 /xy AB}xyKrH" {18.375 0.0 l}xyH" {3072 10 /xy AB}xy=ԶT/urǍ=햟i" {11.8178 11.8178 l}xy=햟T0" {-4096 10 /xy AB}xy'uǍ)'" {0.0 18.8472 l}xy)" {-3072 10 /xy AB}xy N;Lul8;M" {-10.92093 10.91501 l}xy8;M" {-2048 10 /xy AB}xyl ?" {-18.375 0.0 l}xy ?" {-1024 10 /xy AB}xy5`" {mark 72.5903 0.0 36.29515 12.0 0.0 0.0 0.08081 0.46774 q}xyRt$)" {2853 10 /xy AB}xy=" {mark 72.5903 0.0 36.29515 12.0 0.0 0.0 0.53226 0.8247 q}xy:" {mark 72.5903 0.0 36.29515 12.0 0.0 0.0 1.0 0.82465 q}xyUr!ǵf(x):" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 1.0 0.1753 q}xy3᝟ fr 0ncmsy5Zcmr51>" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 0.1753 0.40353 q}xyqi" {-1312 10 /xy AB}xy?" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 0.59647 0.91931 q}xy;" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 1.0 0.91931 q}xytB1.7Sp`eedinguptypesettinguTOneIthingthatyouwillnoticeisthatEXY TI-picissome-times\slowintypGesettingdiagrams(thisistobeex-pGected]consideringthenumber]ofdrawingoperationspGerformed@asre ectedbythenumbGerlastineachxymatrix, message).9If"youfollowedtheruleofstartingallDentrieswitha(nonexpandable)characteror{ ѲthenyouUUcaninsertthedeclarationff2 {Ll\CompileMatrices&ff2 ;in}thepreambleofyourdoGcument:thiswillcreatetem-pGorary les^4%containingc}'ompiled;versionsofeachma-trixthatcanbGeloadedveryquickly;theyareautomat-icallyUUrecreatedwhenamatrixischanged. If.thiscausessomediagramstonotwork,dthensuch compilationcanbGeexplicitlyswitchedo byusing,\xymatrixnocompileinplaceof\xymatrix5lв.Compilation&canbGeswitchedo completelywith\NoCompileMatrices{"(whichrespGectsTU>'ExXgroupingasdoGesUU\CompileMatrices,bytheway). Andifyouarestillnotsatis edwiththespGeedthenyouUUcanaddthefollowing:ff2 {TL\OnlyOutlines&ff2 ;whichkwillomitallcompiledpictures;theadditionalcommand\ShowOutlineswilladdadottedrectangleoutliningUUthesizeofthepicture.[ff^ J= "5-:4LTheStempղwillplacethelabGelatthepointwhere{+}&B}$will>willplacethefollowinglabGelatapoint>{+}&B}$swill ANs,inwhich s.'ExX textaslabGels(aswellasentriestobGeexplainedlater).Theնcharacter*iisreservedforthis:rinitssimplestform+*{i%mathc} 틲will+typGesetthemathmaterialasanob8ject.ѝThisʜislike{ mathc} exceptthatthedefaultstyleUUisignoredandthereisnoaddedblankmargin. However,5ingeneralthefollowingformof*obje}'ctisavqailable:mNff2 ,Q?*W;Thefollowingarethemostycommon, thefulllistofpGossibilitiescanbefoundinUUthereferencemanual[8, g.q3]: Nff2+fgrow+<+dimenc>fgrowUUbydimen+=fgrowUUtoenclosingsquare-fshrink-<+dimenc>fshrinkUUbydimen-=fshrinkUUtocontainedsquare!fdoUUnotcenter[o]fround[l]UU[r][u][d]fadjustUUleft,right,...[F]UU[F=]fps: SDict begin xyc endW(" {0.0 15.70836 -6.0 -15.70836 6.0 ov}xyUUfdframeps: SDict begin xyc end'" {0.0 17.77782 -6.0 -17.7778 6.0 ov}xy'" {0.0 15.77782 -4.0 -15.7778 4.0 ov}xyUUfddoublefd[F.]UU[F--]fps: SDict begin xyc endg32328\3232Q썍3232323232323232323232323232323232323232323232323232Q3232  ΟC3232]2323232323232#C3232]232323232323232g32328\3232Q썍3232323232323232323232323232323232323232323232323232Q3232UUfddotted:ps: SDict begin xyc endg3232" {3072 F d}xy r" {3072 F d}xy pٍ" {3072 F d}xy p" {3072 F d}xypО3232  ." {1024 F d}xy" {1024 F d}xy.$" {1024 F d}xy$" {1024 F d}xy32g3232" {3072 F d}xy r" {3072 F d}xy pٍ" {3072 F d}xy p" {3072 F d}xypО3232UUfddashed[F-,]UU[F-:<3pt>]fps: SDict begin xyc end\s(" {0.0 18.36115 -6.0 -18.36113 6.0 ov}xy3333$玍$33 33UUfdshadedps: SDict begin xyc end (" {3.0 21.12505 -6.0 -21.12503 6.0 ov}xyUUfdrounded.ff2 Sinceob8jectsspGeci edthiswaystartwithnomargin,Ua singleUU+ ꧲isUUusuallyincludedtogetthedefaultspacing.{#ExerciseT7: TypGesetUUps: SDict begin xyc end!ǵA " {0.0 0.0 l}xyGx(" {5.15277 5.15277 5.85764 5.85764 ox}xyx#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!B6@.ꨍ There}canonlybGeoneb}'oxing.ThiscanbeanyboxgenerationUcommand.sThefollowingarethemostuse-fulUUb}'oxing}{"ztext} *combinations: _ff2 A @variant{2tip}m+tipUU(orshaft)ob8ject A \txt{?...}m+ordinaryUUtext A \composite{?...*...}m+combinedUUob8jects A \frm{}m+repGeatUUlastob8jectgʉff2(the:]pGossibilitiesforvariant-5andtiparegiveninthefollowingsection).T Finally*, \hbox{?...}꧟^6c5isaquickwayff^ J= "5-:6LThe{plainTAEMXcommand\hbox7corresp{8q...} 6will:constrainthetexttoacentered6pGcwidecolumn.By:theway*, \txt|ٲcanbGeusedoutsideofXY 2-picconstruc-:tions.;Finally*,fseveralNob8jectscanbGecombinedusingthe:lastkform;.the*sservetoseparatethecompGosedob8ject.0⍒:ExerciseT8: TypGesetUUps: SDict begin xyc end!ǵA  " {2765 st}xy:High :label= " {2765 st}xy5!+5!Ǹ-!Dz+-!Ǹ%"!Dz+%"!Ǹž!Dz+ž!Ǹb!Dz+b!Ǹ !Dz+ !Ǹ>!ǵBP@.:2.3:MorearrowstylesuT:The)arrowstylesdescribGedinsection1.3areallexam-:plesUUofthegeneralarr}'owstyleconstructions: ;ff2 g>@variant{2tail]shaftH-he}'ad}>@variant{2he}'ad}qff2&ՍthatindescribGesarrowswiththeindicatedtail,shaft,andahe}'ad (onthe rstformthetailandheadcanbGeomitted;theusecondstyledefaultstohavingnotailandaUUstandardshaft). TheV}followingpGossibilitiesexistforhe}'ad_andtailwhichUUwewilldenotetips'v(hereshownasheads): qff2 !ɍ<+Ops: SDict begin xyc end:" {-768 10 /xy AB}xy:" {19.76208 4.94052 dt}xyh>wps: SDict begin xyc end:" {3328 10 /xy AB}xy:" {19.76208 4.94052 dt}xyxps: SDict begin xyc end:" {-3686 st}xy|Y5" {-3686 F d}xy:" {19.76208 4.94052 dt}xy<<+Ops: SDict begin xyc end T" {-768 10 /xy AB}xy:" {-768 10 /xy AB}xy:" {19.76208 4.94052 dt}xycS>>wps: SDict begin xyc endɂ" {3328 10 /xy AB}xy:" {3328 10 /xy AB}xy:" {19.76208 4.94052 dt}xy+ps: SDict begin xyc end: " {3328 st}xyV5v" {3328 F d}xy:" {19.76208 4.94052 dt}xy|<+Ops: SDict begin xyc end: " {-768 st}xy:" {-768 10 /xy AB}xy:" {19.76208 4.94052 dt}xycS>|wps: SDict begin xyc end: " {3328 st}xy:" {3328 10 /xy AB}xy:" {19.76208 4.94052 dt}xy|ps: SDict begin xyc end: " {3328 st}xy:" {19.76208 4.94052 dt}xy|<<+Ops: SDict begin xyc end: " {-768 st}xy T" {-768 10 /xy AB}xy:" {-768 10 /xy AB}xy:" {19.76208 4.94052 dt}xy^ >>|wps: SDict begin xyc end: " {3328 st}xyɂ" {3328 10 /xy AB}xy:" {3328 10 /xy AB}xy:" {19.76208 4.94052 dt}xy||ps: SDict begin xyc endii " {3328 st}xy: " {3328 st}xy:" {19.76208 4.94052 dt}xy(+Ops: SDict begin xyc end: " {3328 h}xy:" {19.76208 4.94052 dt}xyh)wps: SDict begin xyc end: " {-768 h}xy:" {19.76208 4.94052 dt}xyops: SDict begin xyc endK O!cmsy7:" {19.76208 4.94052 dt}xy/+Ops: SDict begin xyc end: " {3024 st}xy:" {19.76208 4.94052 dt}xycS//wps: SDict begin xyc endYK " {3024 st}xy: " {3024 st}xy:" {19.76208 4.94052 dt}xyff2ҍandUUtheshaftH-shouldbGeoneofthefollowing: 8ff2ҏ)-9/ps: SDict begin xyc end"$4" {28.14311 9.383 l}xyD--Ēps: SDict begin xyc end"$4" {28.14311 9.383 dd}xya)~9/ps: SDict begin xyc end@K " {3413 g}xyw5 " {3413 g}xyh " {3413 g}xy ") " {3413 g}xyD~~Ēps: SDict begin xyc end " {3413 g}xySO: " {3413 g}xy q\ " {3413 g}xy).9/ps: SDict begin xyc end"$4" {28.14311 9.383 dt}xyjff2TheUUvariantH-shouldbGeemptyoroneofthefollowing: ;ff2 g6N^@VK\abGove"UUvqariant 6N_@VK\bGelow"UUvqariant6N2@VK\double"UUvqariant6N3@VK\triple"UUvqariantqff2&ՍHere~aresomestandardarrowsinthisnotation,SallfromUUAtoBƲasusual:5AAps: SDict begin xyc end@{<->}3 qA>?" {-1024 10 /xy AB}xy>?" {0.0 0.0 l}xy\?" {3072 10 /xy AB}xy\?" {30.00002 0.0 l}xy\?" {0.0 0.0 l}xy_? qB@^{<->}3H*A>? ݀" {-1024 10 /xy B}xy>? ݀" {0.0 0.0 l}xy\? ݀" {3072 10 /xy A}xy\? ݀" {30.00002 0.0 l}xy\? ݀" {0.0 0.0 l}xy_?H*BW@_{<->}3A>?9" {-1024 10 /xy A}xy>?9" {0.0 0.0 l}xy\?9" {3072 10 /xy B}xy\?9" {30.00002 0.0 l}xy\?9" {0.0 0.0 l}xy_?B.c,@2{<->}3.A>?+T" {-1024 /XT tt}xy\?+T" {3072 /XT tt}xyY*T" {25.00002 0.0 l}xyY,T" {25.00002 0.0 l}xy_?.B=@3{<->}3=UA>?:" {3072 F d}xy>?:" {-1024 /Xt tT}xyW?:" {-1024 F d}xy\?:" {3072 /Xt tT}xyY 8" {23.60002 0.0 l}xyY <" {23.60002 0.0 l}xyY :" {23.60002 0.0 l}xy_?=UBLWj:5*tj??gwAs aspGecialconvenience = and :are providedasab- breviationsUUfor- ꧲and.withvqariantforcedto2R. As itcanbGeseen, thevqariantwilla ecttheentir}'earrow.1Sometimesthisisnotwhatiswanted.1Inthatcase'alo}'calivariantcan'bGeusedbyenteringanyofthetail,UUshaft,andhe}'ad,onthefollowingform: Qff2 8VYvariant{2tip}VYvariant{2shaft}~։ff2k덲HereUUaresomearrowswherethisisrequired:z$9ps: SDict begin xyc end@{^{(}->}J? qAT " {3072 ha}xyT" {0.0 0.0 l}xyl" {3072 10 /xy AB}xyl" {23.99998 0.0 l}xyl" {0.0 0.0 l}xyo qBܞ@{|-_{>}}J?H*AT ݀ " {3072 st}xyT ݀" {0.0 0.0 l}xyl ݀" {3072 10 /xy B}xyl ݀" {23.99998 0.0 l}xyl ݀" {0.0 0.0 l}xyoH*B"NoticethatthereisnodistinctionbGetweenshaftsandtipsSusingthisform,thusitisnecessarytoincludeallthreeoftail, shaft,andhe}'ad,whenusingit.*Thead-vqantage5isthatitispGossiblethento\ llwithatip."F*urthermore,]thefollowingadditionalpGossibilitiesareavqailableUUwhenusingthisnotation: S}ff2 /{|-}&ps: SDict begin xyc end: " {3328 st}xy:" {3328 F d}xy:" {19.76208 4.94052 dt}xyRK^{|-}vps: SDict begin xyc end5" {-2816 F d}xy:" {3328 F d}xy:" {19.76208 4.94052 dt}xy$_{|-}Rps: SDict begin xyc end:" {1280 F d}xy:" {3328 F d}xy:" {19.76208 4.94052 dt}xyW{|=}vps: SDict begin xyc end " {3328 st}xy" {3328 F d}xy/ " {3328 st}xy/" {3328 F d}xy:" {19.76208 4.94052 dt}xy$3{|-}Rps: SDict begin xyc endF " {3328 st}xyF" {3328 F d}xy?G " {3328 st}xy?G" {3328 F d}xy: " {3328 st}xy:" {3328 F d}xyF" {19.76208 4.94052 dt}xy?G" {19.76208 4.94052 dt}xy:" {19.76208 4.94052 dt}xy {*}&ps: SDict begin xyc endK:" {19.76208 4.94052 dt}xyW^{`}vps: SDict begin xyc end: " {3328 ta}xy:" {19.76208 4.94052 dt}xyR!_{`}Rps: SDict begin xyc end: " {3328 tb}xy:" {19.76208 4.94052 dt}xyW^{'}vps: SDict begin xyc end: " {-768 tb}xy:" {19.76208 4.94052 dt}xyR!_{'}Rps: SDict begin xyc end: " {-768 ta}xy:" {19.76208 4.94052 dt}xy ff2TheDevenmoregeneralform*Aobje}'ctzcanbGeused,{whereobje}'ct-refers:toanyoftheconstructionsdescribGedinsectionUU2.2.ExerciseT9: TypGesetUUps: SDict begin xyc end qA " {-608 10 /xy B}xy9" {mark 37.7934 0.0 18.8967 12.0 0.0 0.0 1.0 0.17871 q}xy%ԟ{" {2664 10 /xy B}xy=" {mark 37.7934 0.0 18.8967 12.0 0.0 0.0 0.17871 0.81372 q}xy9" {mark 37.7934 0.0 18.8967 12.0 0.0 0.0 1.0 0.81366 q}xy ;Z#2Ɵ! " {3608 st}xy N" {3608 F d}xy*A " {3819 st}xyzK" {3819 F d}xy " {4096 st}xyfS" {4096 F d}xy^A" {-3819 st}xyjIw" {-3819 F d}xy#T!" {-3608 st}xy!W" {-3608 F d}xy( qB:@.2.4SlidingarrowssidewaysuTItHRisoftendesirabletohaveHRseveralparallelarrowsbGe-tweenAtwoob8jects.ThiscanbGedonebyslidingeitherorbGotharrowssidewaysadistancegivenasaTU>'ExXdimen-sionenclosedin@<>s:itspGeci eshowfar\sideways"theUUarrowshouldbGemoved,e.g.,N8\xymatrix{?A\ar@<1ex>[dr]^a_{.}\\&?B\ar@<1ex>[ul]^b\ar@<1ex>[r]^c?&?C\ar@<1ex>[l]^d_{.}}willUUtypGesetIps: SDict begin xyc end qAYb" {0.02487 -0.02586 l}xy ôa_:(" {2074 10 /xy AB}xy(" {24.63425 -24.0 l}xy(" {0.02487 -0.02586 l}xy(%ŵB"s^" {-0.02487 0.02586 l}xyALnb Us#" {-2022 10 /xy AB}xy Us#" {-24.63425 24.0 l}xy Us#" {-0.02487 0.02586 l}xy39(" {0.0 0.0 l}xy=m(cK8(" {3072 10 /xy AB}xyK8(" {23.99998 0.0 l}xyK8(" {0.0 0.0 l}xyN8%ŵCK8&S" {0.0 0.0 l}xy=s.Ĵd>Wݟ#S:39&S" {-1024 10 /xy AB}xy39&S" {-23.99998 0.0 l}xy39&S" {0.0 0.0 l}xy>A"pGositivedistancewillslidethearrowinthe\^?-direction,"is?oftenappropriatesinceitcorrespGondsroughlytotheheightUUofletterslike\x,"inthetypGesizebeingused.h :ExerciseT10: TypGesetUUps: SDict begin xyc end!ǵA8" {mark 33.7934 0.0 16.8967 12.0 0.0 0.0 1.0 0.1997 q}xy#" {2564 10 /xy AB}xy<" {mark 33.7934 0.0 16.8967 12.0 0.0 0.0 0.1997 0.85083 q}xy9" {mark 33.7934 0.0 16.8967 12.0 0.0 0.0 1.0 0.85077 q}xyE" {mark 33.7934 -4.30554 16.8967 7.69446 0.0 -4.30554 1.0 0.1997 q}xy#5" {2566 10 /xy AB}xyI" {mark 33.7934 -4.30554 16.8967 7.69446 0.0 -4.30554 0.1997 0.85083 q}xyF" {mark 33.7934 -4.30554 16.8967 7.69446 0.0 -4.30554 1.0 0.85077 q}xy$!B6@.|:2.5:Moretargets:ThetargetaddresscanbGegiveninalargenumbGerof :formatsERcalledp}'ositions.lqThefullrangeofpGossibilities:isdescribGedinthereferencemanual[8, g.1];hereis:agnumbGerofusefulonesinadditiontothehop Gformat:describGedUUinsection1.3:z;<[*9rG,c]?,;jwhere4r;careintegers,denotesther}'elative[ul]T* \ar@<1ex>[ul];[]?}4 d,whereDx;DygareTU>'ExXdimensions,is  theUUvectorwiththosecoGordinates,T  thefollowing\cornero sets"ofatargetarevec- torsUUasshown:.|nAXtps: SDict begin xyc endu$32323232:z32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:k3232")č(֍3232j32323232323232323232323232323232323232323232323232323232Nq@(֍3232j3232323232323232323232323232323232323232323232323232323232$32323232:z32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:k3232ؽ" {0.0 0.0 dt}xyNq?" {0.0 0.0 dt}xyǍ/$R" {0.0 0.0 dt}xyǍ/$" {0.0 0.0 dt}xyؽ" {-31.29787 0.0 l}xyؽ" {-1024 10 /xy AB}xy8LNq?" {31.29787 0.0 l}xyNq?" {3072 10 /xy AB}xyWARǍ/$R" {0.0 -17.07156 l}xy/$" {1024 10 /xy AB}xy,RDǍ/$" {0.0 17.07156 l}xy/$u" {-3072 10 /xy AB}xy,㝮Uؽ" {-31.29787 -17.07156 l}xyؽ" {-465 10 /xy AB}xycDLNq?" {31.29787 -17.07156 l}xyNq?" {2513 10 /xy AB}xySbcDRؽu" {-31.29787 17.07156 l}xyؽu" {-1583 10 /xy AB}xyULNq?u" {31.29787 17.07156 l}xyNq?u" {3631 10 /xy AB}xySbUR1? (theyUUmustbGespeci edinuppercase),and  /ddimenc/ 4istheve}'ctoragoingdimen7inthepar- ticularAdirectiondwhichcanbGeeithertheeight simplekonesinsection1.6,Bemptytodenotethat thecurr}'entAdirection;(thelastdirectionofanar- row)UUshouldbGeused,oroneofthefollowing:  ff0 9!lva(1, z)I"#absoluteUUangle!ld:a( z)I"#relativeUUangleindegrees!ld:( x,y[)I"#relativeUUvector!ld^UU/d_I"#shortgfor:a(90)$/:a(-90)~׍ ff0q wherethedinthelastfourmaybGeemptytode- noteUUthe\currentdirection."  0UUisthezerovector.|Many*,manymorepGossibilitiesaredescribedintheref-erenceUUmanual[8].Exercise11: Whati^isthedi erencebGetweeni^atargettUUandthetargett+0 ?2.7Arrowspassingundera_Arrows!canpassunder(orvia)anyotherentry:5`Justinsertk't,q9i.e.,aquote(apGostrophe)characterfollowedbyt atarget,foreachentrythatshouldbGevisitedexcepttheUUlast,\ordinary& nal"entry:N8\xymatrix{Q{\circ}\ar@{|-->}?'[dr]^a4P'[rr]+D*{\bullet}?^b9[drrr]?^cP&?{\circ}&{\circ}&{\circ}\\Q{\circ}?&{\circ}&{\circ}&{\circ}} typGesets |,}ps: SDict begin xyc endڪ Ɵڪ " {2064 st}xy :߉" {0.0174 -0.01903 dd}xyT ڪa#2:ڪ" {24.3924 -24.0 dd}xyI4CwbI " {26.99998 22.54253 dd}xy_4wci}M" {2217 10 /xy AB}xyi}M" {26.99998 -22.55034 dd}xyi}M" {0.02907 -0.03276 dd}xy&ڪIڪlڪ"Lp&"LpI"Lpl"Lp4AsUUyousee,labGelsaresetseparatelyoneachsegment.gw:ExerciseT12: TypGesetUUthe\lambGdacube"h-S ps: SDict begin xyc endW!, " {0.0 0.0 l}xyI" {28.94374 0.0 l}xyI" {0.0 0.0 l}xyǍ"꬟x" {0.0 0.0 l}xyǍ"꬟" {0.0 -14.52779 l}xyǍ"꬟( " {0.0 -13.52783 l}xyǍ"꬟( " {0.0 0.0 l}xyLCǍR꬟x" {0.0 0.0 l}xyǍR꬟( " {0.0 -34.05562 l}xyǍR꬟( " {0.0 0.0 l}xy2Ǎc" {0.0 0.0 l}xyǍqɟx" {11.05557 11.05557 l}xyǍqɟx" {0.0 0.0 l}xyUX" {0.0 0.0 l}xy.r" {27.26212 0.0 l}xy.r" {0.0 0.0 l}xyǍ ꬟x" {0.0 0.0 l}xyǍ ꬟A" {0.0 -35.05557 l}xyǍ ꬟A" {0.0 0.0 l}xy1rPc2ǍAc" {0.0 0.0 l}xyǍLqɟx" {11.05557 11.05557 l}xyǍLqɟx" {0.0 0.0 l}xyǍ:꬟x" {0.0 0.0 l}xyǍ:꬟A" {0.0 -35.05557 l}xyǍ:꬟A" {0.0 0.0 l}xyW0!feT, -" {0.0 0.0 l}xy7꬟-" {11.79166 0.0 l}xyEȟ-" {7.88715 0.0 l}xyEȟ-" {0.0 0.0 l}xyHȟ0Pc!cfeTI!XE" {0.0 0.0 l}xy1rE" {27.26212 0.0 l}xy1rE" {0.0 0.0 l}xyǍcA" {0.0 0.0 l}xyǍq̟7x" {10.05562 10.05562 l}xyǍq̟7x" {0.0 0.0 l}xy4rIPǍAcA" {0.0 0.0 l}xyǍKq̟7x" {10.05562 10.05562 l}xyǍKq̟7x" {0.0 0.0 l}xy_ٍ:Hintز:$\goingunder"anemptyentryleavesasmallgap :atpthatloGcation.Thecompactnessisachievedpusinga:trickUUdescribGedinsection3.3.!%:2.8:Moreb`endingarrowsD0:Finally*,EarrowscanbGendaroundentries:CHjustinsert:`dt,i.e.,abackquoteandadirectiondfollowedby:atargett,foreach\turn"thatstartsoutinthed-:directionandendsinaquarterturntowardsthetar-:get@st.jThisisdi erentfromthecurvingdescribGedear-:lierinthatallturnsconsistofastraightpartending:inקaturnwhichisamultipleof׫1/8circlesegments,and:eachUUsegmentallowsseparatelabGels. ;The#pGossibledirectionsarethoseofsection1.6and:2.6,andthepGossibletargetsincludeallthosediscussed:abGove.ݒActuallyΙthedirectionisonlyrequiredforthe: rstPinaseriesofturnssincethe naldirectionofone:turnistheobviouschoiceforthefollowingturn.aF*ur-:thermore,;turnszcanbGechangedfromthedefaultby:addingeither^dforanticloGckwiseturntodor_dfor:cloGckwiseturntod,wheredisthe\exitdirection"of:theUUturn.;Finally*,2the|turnswillhave|radius10ptbydefault,:but\thiscanbGechangedtoanydimensionRoղfromapar-:ticularDyturnandonwardsDybyinserting/RX@immediately:aftero!the``^<#Y|(Vox+/()[]R> g6}{%?!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}}de nesUUanewtipthatmakes\xymatrix{?A\ar@{=|>}[r]&B}typGesetps: SDict begin xyc end qA " {0.0 0.0 l}xy " {0.0 0.0 l}xy#@ " {3072 st}xy'" {2867 10 /xy A}xy'" {3277 10 /xy B}xy#@" {21.74998 0.0 l}xy#@" {21.74998 0.0 l}xy( qB;u.@Noticehowthe\relativedirec-tion"ĤisusedheretorotatesomeofthecompGosedcom-pGonents.gw:Exercise 14: OftenMtipsusedas\tails"haveMtheirink :onOthewrongsideofthepGointwheretheyareplaced.:F*ortunatelyOPspace( )isalsoatipcharactersowecan:de neǧthedirectional >togeneratea\tail-spaced":arrow.qDoUUthissuchthatN8:\xymatrix{?A\ar@{>->} @<2pt>[r]+*\ar?@{>->}@<-2pt>[r]&B}i+:typGesets PٍCps: SDict begin xyc end qA " {3072 10 /xy AB}xy " {0.0 0.0 l}xy%" {3072 10 /xy AB}xy%" {23.99998 0.0 l}xy%" {0.0 0.0 l}xy" {3072 10 /xy AB}xy%" {3072 10 /xy AB}xy%" {21.49998 0.0 l}xy%" {0.0 0.0 l}xy( qBPٟ ;Finally*,*whenXY -picdiagramsareusedinconjunc-:tioniwithKnuth'sc}'omputermodernfonts;Ӳthenithedec-:laration: Lff2 WG,\SelectTips?{cm}{}ff2'willUUchangethetipstosomethatloGoksimilar,e.g.,$\SelectTips{cm}{}?\xymatrix@1{A\ar@{->>|}[r]&B}$HtypGesetsps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy# " {3072 st}xy!" {3072 10 /cm AB}xy#" {3072 10 /cm AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!B/9.WThesecondargument(here{}!) canbGeusedtospecifyapointsize{10},{11},or{12},ifqdesired(thedefaultis{10}q^7w);~{cm}canbGereplacedby:{eu}hand:{xy}to:gettipsin\Euler"andthedefaulttechnicalstyle,respGectively*.ThedeclarationrespGectsTU>'ExXUUgrouping.Exercise5c15: TypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy" {3072 10 /cm AB}xy" {3072 10 /cm AB}xy" {10.99998 0.0 l}xy#" {3072 10 /eu AB}xy#" {11.0 0.0 l}xy#" {3072 10 /xy AB}xy#" {0.0 0.0 l}xy#" {0.0 0.0 l}xy$!B6.l]Hintز:Withtheconstruction\objectobje}'ctonecantypGesetanXY K-picobje}'ct(anything Cthatcouldfollowa* Tinsection2.2)inUUanycontext.!3LMoreffEntriesCThissectionexplainswhatcangoinanentryandhowtheUUgeneralformoftheentriesischanged.13.1Manualentryformatting|AllRtheentrieswehaveseenthusfarhavebGeensimplemathob8jects.* However,itispGossibletochangetheformatUUofanindividualentrybyusingtheform: ff2 WVj,*obje}'ctH-arrowsff2'Thisxallowscompletecontroloverwhatob8jectisplacedinLtheentry*,NloverridingLanyspacingandotherconven-tions*fortheentry*.GThiswashowtheframewasob-tainedUUinthe gureinsection1.2.  A*simple+useofthisistoinserttextinentriesus-ing-\txtob8jectsjustlikelabGelsasdescribedabove-insectionUU2.2:2ff^ J= "5-:7LExcept]whenXs0`Y l-picisloadedasaL#A TAEMXFd2"_pacÎkagewhere theXdefaultsizeisused.LWj:8 N{*tj??gw\xymatrix{ Q*\txt{A?verylongandstupid\\program}\ar[rr]^-{\txt{weird\\arrow}}Q&&*\txt<2pc>{Com\-pli\-cated\\Code}}ɍwillUUtypGeset)퍍 ps: SDict begin xyc endōAUUverylongandstupid  *\txt<8pc>{%?This?isaverybigcommentary?but?itdoesnototherwiseaffect?the?diagram.}?\ar[l]?\ar[d]\restore\\?&B\ar@{-}[r]&C\ar@{-}[r]&D}willUUtypGeset&y/ps: SDict begin xyc end qA Z" {0.02487 -0.02586 l}xy% q" {24.63425 -24.0 l}xy% q" {0.02487 -0.02586 l}xy̍[pThisU>isaverybig XcommentaryU>butitY#YdoGesU>nototherwiseXWa ectU>thediagram.ǍQ" {0.0 -0.00002 l}xy " {-1024 10 /xy AB}xy " {-68.40166 0.0 l}xyǍ " {0.0 -0.00002 l}xyQY" {-0.01463 0.0 l}xy39l" {-582 10 /xy AB}xy39l" {-30.31487 -13.07436 l}xy39l" {-0.00331 0.0 l}xy(%ŵB39"w" {0.0 0.0 l}xyK8"w" {23.99998 0.0 l}xyK8"w" {0.0 0.0 l}xyN8%CYs"w" {0.0 0.0 l}xyqs"w" {24.0 0.0 l}xyqs"w" {0.0 0.0 l}xyts%D=rItWcanbGereplacedbyanyof+,x+=,-,and>W-=ofsec-tionO2.2withthesamemeaning,Αi.e.,replaceO\set"with6\increase,"1\increasetoatmost,"\decrease,"and\decreasetoatleast,"xrespGectively*.uNForexample,$\xymatrix@1@=0pt@M=0pt{A&B\\C&D}$5inthetexttypGesetsps: SDict begin xyc end.g!ǵA!B !CП !Dke. In?caseuniformZsp}'acing" isdesired,wseveralalternativeformsUUexist. >ff20Q@!EHforceUUallspacesequal0Q@!0EH|UUandignoreentrysizes0Q@!REHforceUUequalrowspacing0Q@!CEHforceUUequalcolumnspacingljff2Finally=aspGecialnotationallowsr}'otationofanentirematrix: >ff22@dC۲rotateUUtowardsdljff2Only#thematrixgridwillrotate,however,not#theac-tualUUcontents.ExerciseT17: TypGesetUUthe\striplemma"؍Vps: SDict begin xyc end Şa(hˉ" {0.0204 -0.01035 l}xy1 ›" {2048 10 /xy AB}xy1 ›" {8.9871 -8.97546 l}xy1 ›" {0.02042 -0.0072 l}xyǍ{A'" {0.0 0.0 l}xy ik" {0 10 /xy AB}xy Jz" {0 10 /xy AB}xyǍ JW" {-20.1898 -20.1898 l}xyǍ JW" {0.0 0.0 l}xy4yşG+a^0Ǎ11d" {0.0 0.0 dt}xy"(Vj" {0 10 /xy AB}xy *uy" {0 10 /xy AB}xyǍ ,Ӳ" {-17.18088 -17.18088 dt}xyǍ ,Ӳ" {0.0 0.0 dt}xyb MP!H" {0.01035 -0.02042 dt}xy\(X" {2048 10 /xy AB}xy|*w" {2048 10 /xy AB}xy|*w" {9.19272 -9.20416 dt}xy|*w" {0.00761 -0.02042 dt}xy|43b^0Bi 3.4EntrystyleuTAs0mentionedabGove,&theentriesofadiagramaresetinmathmoGdeintextstyle.2Y*oumaychangethisbyrede niningthemacro\objectstyle, QandthelabGelstyle%byrede ning\labelstyle.Q W*ecancombinethiswithUUtheabGoveUUtoget\smalldiagrams,"e.g.,typingN8$\left(?\def\objectstyle{\scriptstyle}LWj:9 l*tj??gwQ\def\labelstyle{\scriptstyle} Q\vcenter{\xymatrix?@-1.2pc@ur{A?\ar[r]^{a} &B\ar[d]^{b}\\A'\ar[u]^{a'}?&B'\ar[l]^{b'}}}\right)$"inUUaparagraphwilltypGeset\V0BBfi@ps: SDict begin xyc enddDA f " {0.0 0.0 l}xy Ka2" {-4096 10 /xy AB}xy2" {7.8005 7.8005 l}xy2" {0.0 0.0 l}xyf8BС" {0.01767 -0.00713 l}xy$+twb$ȟ" {2048 10 /xy AB}xy$ȟ" {6.79932 -6.78827 l}xy$ȟ" {0.01767 -0.00613 l}xyAr0,̟ ,~" {-0.01767 0.00613 l}xyݟգar0 ddD" {-2048 10 /xy AB}xy ddD" {-6.79932 6.78827 l}xy ddD" {-0.01767 0.00713 l}xy&dDBW=r0$NdD" {0.0 0.0 l}xy$`nϴbr0 ." {0 10 /xy AB}xy ." {-6.78827 -6.78827 l}xy ." {0.0 0.0 l}xyV:d1:dC:dCfi:dACe."6 Y*ou;canevenabandontheuseofmathmoGdeentirely:thescommand\def<\objectstyle[Z{\hbox}KwillchangetheUUformatofentriestoplaintext. ō Similarly*,allentriesarerectangularbydefault,butit ispGossibletochangethistor}'oundbydeclaringthedefaultDjmo}'di erstobGeappliedtoallentriesthatdonotUUoverridethem(cf.section2.2):N8\entrymodifiers={++[o][F-]}\SelectTips{cm}{}\xymatrix?@-1pc{Q*\txt{start}?\ar[r]Q&?0\ar@(r,u)[]^b\ar[r]_aQ&?1\ar[r]^b\ar@(r,d)[]_aQ&?2\ar[r]^b\ar?`dr_l[l] `_ur[l]_a[l]Q&*++[o][F=]{3}\ar?`ur^l[lll]`^dr[lll]^b[lll]\ar?`dr_l[ll]`_ur[ll][ll]}willUUtypGeset(,s!ps: SDict begin xyc endstart" {0.0 0.0 l}xy " {3072 10 /cm AB}xy " {12.0 0.0 l}xy " {0.0 0.0 l}xyn)#(" {9.22223 9.22223 8.50002 8.50002 ox}xy&ګ0 QȟM" {mark 30.81949 0.0 66.81949 0.0 30.81949 36.0 30.81949 0.0 1.0 0.0957 bz}xy0N8b*>i" {712 10 /cm AB}xy QȟQ" {mark 30.81949 0.0 66.81949 0.0 30.81949 36.0 30.81949 0.0 0.0957 0.89294 bz}xy QȟN" {mark 30.81949 0.0 66.81949 0.0 30.81949 36.0 30.81949 0.0 1.0 0.89294 bz}xy5x[Ua=" {3072 10 /cm AB}xy=" {12.0 0.0 l}xy=" {0.0 0.0 l}xynF#(" {9.22223 9.22223 8.50002 8.50002 ox}xyCګ1RtǴbZ" {3072 10 /cm AB}xyZ" {12.0 0.0 l}xyZ" {0.0 0.0 l}xy QȟN" {mark 59.81953 0.0 95.81953 0.0 59.81953 -36.0 59.81953 0.0 1.0 0.0957 bz}xyLM%!aG>" {-2760 10 /cm AB}xy QȟR" {mark 59.81953 0.0 95.81953 0.0 59.81953 -36.0 59.81953 0.0 0.0957 0.89294 bz}xy QȟO" {mark 59.81953 0.0 95.81953 0.0 59.81953 -36.0 59.81953 0.0 1.0 0.89294 bz}xync#(" {9.22223 9.22223 8.50002 8.50002 ox}xy`ګ2owǴbw" {3072 10 /cm AB}xyw" {12.0 0.0 l}xyw" {0.0 0.0 l}xybQ B" {10.0 -90 45 o}xyicߟ" {0.00612 -0.00612 l}xyic" {0.00615 -0.00615 l}xyF " {10.0 135 270 o}xyRx(xaF" {-27.36179 -0.00166 l}xy?O " {-4096 10 /cm AB}xyǍ?O@F" {0.00171 0.00171 l}xyǍ?O@F" {0.0 0.0 l}xyn#(" {9.22223 9.22223 8.50002 8.50002 ox}xyn#(" {7.22223 7.22223 6.50002 6.50002 ox}xy}ګ3QOL" {10.0 -45 90 o}xyǍc" {0.00002 0.00002 l}xyǍc" {0.00005 0.00005 l}xy)N" {10.0 90 225 o}xyR>+b)N" {-85.36188 0.00166 l}xy"La" {2048 10 /cm AB}xy"ݟc" {0.00783 -0.00783 l}xy"La" {0.00002 -0.00002 l}xyQ B" {10.0 -90 45 o}xyc" {0.00612 -0.00612 l}xyc" {0.00615 -0.00615 l}xyF " {10.0 135 270 o}xyF" {-56.36183 -0.00166 l}xy?O " {-4096 10 /cm AB}xyǍ?O@F" {0.00171 0.00171 l}xyǍ?O@F" {0.0 0.0 l}xy(pNoticeдhowweobtainthedoubleringusingthe*obje}'ctform~ whichthenhastoincludeallthedesiredmoGdi ers(and!howtheuseofcomputermoGderntipsisnicefordiagramsUUasthese). 03.5Namingforlateruseastargets㉍If|youbuildanentrywithalongandcomplicatedex-cursionthenyoumightwishtobGeabletorefertoitlater.XYr-picPprovidesamechanismforthis:ǽthereisaspGecialUUtargetformwhichwehaven'tdiscussedyet: ḉff2 +)^%tUU="?name["ljff2{RThisywillintroGducethenewtarget"name[" z4whichwillreferm[tothetargetjustbGeforethe=X.$tThisisparticularlyuseful insideexcursions,Oofcourse,andcanalsobGeusedafterUUlabGels. LڍExerciseT18: TypGesetUUps: SDict begin xyc end qA " {0.0 0.0 l}xyzVǴa%" {3072 10 /xy AB}xy%" {23.99998 0.0 l}xy%" {0.0 0.0 l}xy( qB39" {0.0 0.0 l}xy=ŻǴbK8" {3072 10 /xy AB}xyK8" {23.99998 0.0 l}xyK8" {0.0 0.0 l}xyN8 qCJ" {mark 56.78072 5.43054 37.4637 16.96288 18.8967 4.50694 1.0 0.13892 q}xy:/h" {2630 10 /xy AB}xyN" {mark 56.78072 5.43054 37.4637 16.96288 18.8967 4.50694 0.13892 0.87659 q}xyJ" {mark 56.78072 5.43054 37.4637 16.96288 18.8967 4.50694 1.0 0.87659 q}xy\Y.gw:3.6:Groupingobjectsu:Sometimes{youwishtoframeorotherwisetreatarect- :angleofob8jectsasasingleobject.-ThisispGossiblewith:thelasttwotargetpGositionformsthatwewillmention:: ff2 "Ӎ1t.?sDămergeUUtwithsimples1{6t}DămakeUUtsimpleqff2jThe rstwillenlargettoalso\cover" the\simple"s,(simplemeansthatitcannothave,changesetc.at-tachedunlessencapsulatedin{} .s).:HereisanexamplewhereUUwemergeandframe:N8\xymatrix?@R=1pc{?1,1&1,2&1,3&1,4&1,5\\?2,1&2,2&2,3&2,4&2,5?\save"1,2"."2,4"*[F.]\frm{} \ar"1,1"?\ar"2,1"\ar"1,5"\ar"2,5"?\restore} willUUtypGesetxލP*ps: SDict begin xyc end1;1/qƞ1;2[㌞1;3UR1;41;5EV2;1/qƟEV2;2[㌟EV2;3UREV2;4EV2;5l,Q3232-93232:+32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:3232(=,7xn3232323232323232323232323232323232323232323232323232323232323232323232323232n323232323232323232323232323232323232323232323232323232323232323232323232323232,Q3232-93232:+32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:3232,j" {0.0 0.0 l}xyqǟ" {-1024 10 /xy AB}xyqǟ" {-23.97221 0.0 l}xyqǟ" {0.0 0.0 l}xy,j" {0.0 -0.00003 l}xyqǟ" {-416 10 /xy AB}xyqǟ" {-23.97221 -14.23354 l}xyqǟ" {0.0 -0.00003 l}xy" {0.0 0.0 l}xy" {3072 10 /xy AB}xy" {24.02776 0.0 l}xy" {0.0 0.0 l}xyC" {0.0 -0.08684 l}xy" {2869 10 /xy AB}xy" {24.02776 -4.82669 l}xy" {0.0 -0.08685 l}xy4Asmyoucansee,sthecenterofthemergedob8jectisthesameUUastheoneofthetargetb}'eforetheUU\.?." o FinallyQamoreadvqancedexamplewherewecreatetwo$mergedob8jectswithcenterintheir\real"center,name themandthenconnecttothem.ItalsoshowshowxmacroscanbGeusedinsidediagrams:%theyshouldalwaysUUexpandto\commands"like\arL...,UUetc.:33ps: SDict begin xyc end.f qAdL0" {0.0 26.1191 -25.17557 -26.1191 25.17557 ov}xy g" {0.0 0.0 l}xy&" {3072 10 /xy AB}xy&" {24.4163 0.0 l}xy&" {0.0 0.0 l}xy) qBǍ-$j" {0.0 0.0 l}xy-$" {1024 10 /xy AB}xyǍ-$" {0.0 -24.68451 l}xyǍ-$" {0.0 0.0 l}xyOşdA^0di{2" {0.0 28.92465 -25.51782 -28.92465 25.51782 ov}xy\" {0.0 0.0 l}xyuR" {3072 10 /xy AB}xyuR" {24.41629 0.0 l}xyuR" {0.0 0.0 l}xyxRdBq^0Ǎ}ʟH" {0.0 0.0 l}xy}ʟd" {1024 10 /xy AB}xyǍ}ʟH" {0.0 -24.0 l}xyǍ}ʟH" {0.0 0.0 l}xy&CǍf" {0.0 0.0 l}xyf q" {-3072 10 /xy AB}xyǍfj" {0.0 24.68451 l}xyǍfj" {0.0 0.0 l}xy(̟&D%̟#&W" {0.0 0.0 l}xy ̟#&W" {-1024 10 /xy AB}xy ̟#&W" {-24.0 0.0 l}xy ̟#&W" {0.0 0.0 l}xyOk`&C^0ǍTH" {0.0 0.0 l}xyTd" {-3072 10 /xy AB}xyǍTH" {0.0 24.0 l}xyǍTH" {0.0 0.0 l}xyxd&蟵DG^0ud#&W" {0.0 0.0 l}xy]e#&W" {-1024 10 /xy AB}xy]e#&W" {-23.99998 0.0 l}xy]e#&W" {0.0 0.0 l}xy4k` t" {0.0 0.01146 dt}xyuR9N" {3265 10 /xy AB}xyuR9N" {64.90309 12.24417 dt}xyuR9N" {0.0 0.01146 dt}xyLş"" {3267 10 /xy AB}xyLş"" {62.73817 11.93091 dd}xyLş"" {0.02504 0.0 dd}xy?SDcanUUbGetypesetbyN8\def\g#1{\save?[].[dr]!C="g#1"*[F]\frm{}\restore}%\xymatrix{?\g1A\ar[r]&B\ar[d]&\g2A'\ar[r]&B'\ar[d]\\?C\ar[u]&D\ar[l]&C'\ar[u]&D'\ar[l]?\ar@{.>} "g1";"1,4"?\ar@{-->}"2,1";"g2"} Thenwecanmakearrowsfrom/tothetwoframesbyusingUUthetwoUUnewtargets"g1"and"g2"asshown.#4-Exercise"19: ChangethelambGdacubeofexercise12suchnitisenclosedinatransparent(i.e.,5&dotted)cubGe.LW910 *tj??gw4]Availability½andFfurtherInfor-]mation1WBelow'ExX͡ ffͤ fffd랲cθ "$fd1991{1996 Kristo erUUH.Rose^| ffͤ fffd랲cθ "$fd1994{1996 RossUUMoGore5, ffffߎ(d TheXY-picpackqageisfreesoftware;?;you can+redistributeitand/ormoGdifyitunderthe termsoftheGNUGeneralPublicLicenseas publishedu_bytheF*reeSoftwareF*oundation; eithereversion2oftheLicense,or(atyour option)UUanylaterversion. '㍑ TheQXY8U-picUpackqageisdistributedinthe hopGeDKthatitwillbeuseful,butwithoutoany warr}'anty};Dwithout<-eventheimpliedwarranty ofmer}'chantabilityor tnessHkforaparticular purp}'ose. SeeatheGNUaSGeneralPublicLicense forUUmoredetails. 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:structedN8:\xymatrix@!0{*7&?\lambda\omega\ar@{-}[rr]\ar@{-}'[d][dd]1&?&\lambdaC\ar@{-}[dd]:\\*7\lambda2?\ar@{-}[ur]\ar@{-}[rr]\ar@{-}[dd]*7&?&\lambdaP2\ar@{-}[ur]\ar@{-}[dd]:\\*7&?\lambda\underline\omega\ar@{-}'[r][rr]1&?&\lambdaP\underline\omega:\\*7\lambda{\to}?\ar@{-}[rr]\ar@{-}[ur]*7&?&\lambdaP\ar@{-}[ur]:}[;A7spGecialgthingisadded:P@!.forcesrowsandcolumns:toCbGeequallyspacedasdiscussedinsection3.3;@!0:furthermoremakesthespacingignoretheentrysizes,:givingEacompletely xedgrid.lThegapscouldalsobGe:madewiththe!\...ƽcrossingnotationofexercise6last:inUUsection2.1buttheabGoveUUisshorter.W̍:Answ9erTtoexercise13(p.8): TheUUauthortypGed:\xymatrix@1{*7A?\ar@<-2pt>`d[r]`[r][r]1\ar@<+2pt>?`d[r]`[r][r]&B}:Answ9erTtoexercise14(p.8): TheUUauthorused:\newdir{?>}{{}*!/-5pt/@{>}}:Answ9erTtoexercise15(p.8): TheUUauthortypGed:\xymatrix@1{ *7A?\ar[r]|-{\SelectTips{cm}{}\object@{>>}}j|>{\SelectTips{eu}{}\object@{>}}*7&?B}:Answ9erTtoexercise16(p.9): TheUUauthortypGed:\xymatrix{*7*=0{\bullet}*7\ar@/^/[dr]!U|1*7\ar@/^/[drr]!U|2*7\ar@/^/[drrr]!U|3:\\*7&*+[F]\txt{x}*7&*+[F]\txt{x\\x}*7&*+[F]\txt{x\\x\\x}:}:Answ9erYtoexercise17(p.9): Thegauthorentered:theUUdisplay:\xymatrix@dr@C=1pc{LW913X*tj??gwQa?\ar[r]\ar@{->>}[d]&a'\ar@{.>>}[d]\\ Qb?\ar@{.>>}[r]$&b'}!dAnsw9erTtoexercise18(p.10): TheUUauthortypGedN8\xymatrix{QA?\ar[r]^a="a"&B\ar[r]^b="b"&C\ar?@/^/"a";"b"}㚍NoticetheuseofbGothexplicitbaseandtargetinthearrowUUbGetweenthelabGels.ōAnsw9erNtoexercise19(p.10): ThekauthoraddedtheUQXY U-coGde\save?[].[dd].[ddrr].[rr]*[F.]\frm{}="back"Q\restore㚍 inUUtheentrywith![ٲ,andQ\save?[].[dd].[ddrr].[rr]*[F.]\frm{}\ar@{.}?+UL;"back"+UL\ar@{.}+UR;"back"+UR\ar@{.}?+DL;"back"+DL\ar@{.}+DR;"back"+DR\restore㚍 inUUtheentrywith2toproGduce*č6yps: SDict begin xyc endW!, " {0.0 0.0 l}xyI" {28.94374 0.0 l}xyI" {0.0 0.0 l}xyǍ"꬟x" {0.0 0.0 l}xyǍ"꬟" {0.0 -14.52779 l}xyǍ"꬟( " {0.0 -13.52783 l}xyǍ"꬟( " {0.0 0.0 l}xy(čQ3232h3232C32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232C3232=㍍KZ32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232` $KZ3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232Q3232h3232C32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232C3232LCǍR꬟x" {0.0 0.0 l}xyǍR꬟( " {0.0 -34.05562 l}xyǍR꬟( " {0.0 0.0 l}xy2Ǎc" {0.0 0.0 l}xyǍqɟx" {11.05557 11.05557 l}xyǍqɟx" {0.0 0.0 l}xyUX" {0.0 0.0 l}xy.r" {27.26212 0.0 l}xy.r" {0.0 0.0 l}xyǍ ꬟x" {0.0 0.0 l}xyǍ ꬟A" {0.0 -35.05557 l}xyǍ ꬟A" {0.0 0.0 l}xy% hX3232荍3232332323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323{3232<捍NB׍32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232D؟B׍3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232hX3232荍3232332323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323{3232Ǎ8" {0.0 0.008 dt}xyǍ" {23.20692 23.98546 dt}xyǍ" {0.0 0.008 dt}xyD`% " {0.00209 0.0 dt}xy` #(" {27.29022 23.98546 dt}xy` #(" {0.00209 0.0 dt}xyL{" {0.0 0.00522 dt}xy5" {23.20692 22.9855 dt}xy5" {0.0 0.00522 dt}xyDןL" {0.0 0.0127 dt}xy` #5" {27.29022 22.9855 dt}xy` #5" {0.0 0.0127 dt}xy1rPc2ǍAc" {0.0 0.0 l}xyǍLqɟx" {11.05557 11.05557 l}xyǍLqɟx" {0.0 0.0 l}xyǍ:꬟x" {0.0 0.0 l}xyǍ:꬟A" {0.0 -35.05557 l}xyǍ:꬟A" {0.0 0.0 l}xyW0!feT, -" {0.0 0.0 l}xy7꬟-" {11.79166 0.0 l}xyEȟ-" {7.88715 0.0 l}xyEȟ-" {0.0 0.0 l}xyHȟ0Pc!cfeTI!XE" {0.0 0.0 l}xy1rE" {27.26212 0.0 l}xy1rE" {0.0 0.0 l}xyǍcA" {0.0 0.0 l}xyǍq̟7x" {10.05562 10.05562 l}xyǍq̟7x" {0.0 0.0 l}xy4rIPǍAcA" {0.0 0.0 l}xyǍKq̟7x" {10.05562 10.05562 l}xyǍKq̟7x" {0.0 0.0 l}xytoReferences[1]CAdobGeSystemsIncorporated.HPostScript(L}'anguageCR}'eferenceManual,UUsecondedition,1990.U[2]CDonaldE.Knuth.4TheTKß'E-Xb}'ook.Addison-W*esley,C1984.[3]CLeslieLampGort.L雍Q,t}\cmti7ATKß'E-X|A Do}'cument PreparationCSystem.nAddison-W*esley,UU2ndedition,1994.[4]CRoss>R.MoGore.$sT;yp}'esettingNeuralNetsusing=XY -Cpic,UU1994.nAvqailablethrough[5].[5]CKristo erH.Rose.|TheXY -pichomepage.hurl:Chttp://www.diku.dk/users/kris/Xy-pic.htmli.[6]CKristo erbKH.Rose. UHowtotypGesetprettydia-CgramarrowswithTU>'ExX|designdecisionsusedin?XY C-pic. blInTJiuUrqZlatuxskqa,_editor,Eur}'oTKß'E-Xj='92|CPr}'oceedings~ofthe7thEur}'opean~TKß'E-XConfer}'ence,CpagesQ183{190, Prague,Czechoslovqakia, SeptembGerC1992.UUCzechoslovqakTU>'ExXUsersGroup.gw:[7]xuKristo erԧH.Rose.)XY --picandnotationforcategor- xuical=diagrams.InvitedtalkatECCT-94,uJuly1994.xuAvqailableUUthrough[5].:[8]xuKristo erVqH.RoseandRossR.MoGore.lXY -picR}'ef-xuer}'enceManual.KDIKU,{UniversityofCopGenhagen,xuUniversitetsparken 1,;DK{2100KbGenhavn,3.0xuedition,UUJune1995.:[9]xuMichaelMD.Spivqak.-TheJoyofTKß'E-X|AGourmetxuGuidetoT;yp}'esettingwiththeAU>'M S-TKß'E-XMacroxuPackage.jAmericanMathematicalSoGciety*,*hsecondxuedition,UU1990.-/:Index2ߍ:!,UU5,6,8 :!{;},UU4:&,UU2:',UU7:(,UU5:(),UU4:(0),UU4:(1),UU4:),UU5:*,UU5,6,8,11:+,UU5,6,9:+=,UU5,9:-,UU3,5,6,9:--,UU5:-=,UU5,9:.,UU5:/,UU5,7://,UU5::(),UU7::a(),UU7:;,UU6:<,UU4,5:<<,UU4,5:=,UU9,10:>,UU4,5:>>,UU4,5:>>|,UU5:>|,UU5:@,UU3,5,9:@!,UU9:@(,UU4:@/^/,UU3:@/_/,UU3:@1,UU3:@<>,UU6:@=,UU9:@C=,UU9:@H=,UU9:@L=,UU9LW914gʠ*tj??gw@M=,UU9 /@R=,UU9@W=,UU9@{},UU3[F-,],UU5[F--],UU5[F-:<3pt>],UU5[F.],UU5[F=],UU5[F],UU5[],UU2,6[d],UU5[l],UU5[o],UU5[r],UU5[u],UU5\\,UU2,5^,UU3{5,7^{'},UU6^{`},UU6^{|-},UU6_,UU3{5,7_{'},UU6_{`},UU6_{|-},UU6`,UU7{*},UU6{|-},UU6{|=},UU6|,UU3{5|<,UU5|<<,UU5,11||,UU5~,UU5~~,UU52cell,UU123{|-},UU6^g0,UU7absoluteUUangle,7 /absoluteUUentry*,6adjust,UU5adjustingUUpGosition,6\apit?,UU11\ar?,UU2,4arc,UU12arrow,UU2,4arrowUUhead,5arrowUUpassingunder,7arrowUUshaft,5arrowUUstyle,3,5arrowUUtail,5^gbaseUUentry*,2,6bGend,UU7\bpit?,UU11break,UU3gw:centered,UU5 5:changingUUpGosition,6:changingUUturnradius,7:circleUUsegments,7:circular,UU10:columns,UU2,6:combinedUUob8jects,5,8:commutativeUUdiagrams,1,4:compatibility*,UU11:\CompileMatrices?,UU4:\composite?,UU5,8:computerUUmoGdernfonts,8:coGordinates,UU2:COPYING,UU11:copyright,UU11:cover,UU10:crossingUUarrows,4,7:cubGe,UU7:currentUUdirection,7:currentUUentry*,6:curve,UU3,7ߍ:d,UU2:dashedUUarrow,5:dashedUUframe,5:defaultUUmoGdi er,10:defaultUUspacing,5:de ningUUarrows,8:degrees,UU7:directedUUgraphs,11:direction,UU4,7:directionals,UU8:dottedUUarrow,5:dottedUUframe,5:doubleUUarrow,5:doubleUUframe,5:elliptical,UU10:entriesUUoutsidematrix,9:entriesUUwithtext,8:entry*,UU2,8:entryUUformat,8:entryUUoutsidematrix,3:entryUUstyle,9:excursion,UU9:explicitUUpGositioning,4:extraUUentries,9:format,UU8:frame,UU5:freeUUsoftware,11:\frm?,UU5:ftp,UU11:GNUUUGeneralPublicLicense,11:goingUUaround,8:graph,UU11:grouping,UU10LW915ʠ*tj??gwgrow,UU5g*halfUUarrow,5 \hbox?,UU5head,UU5\hole?,UU3hop,UU2,6intersects,UU4invisibleUUarrow,3\jot?,UU4knot,UU11l,UU2labGel,UU3,4,7labGelUUcenteredonarrow,3labGelUUstyle,9labGelUUwithanyob8ject,5labGelsUUastargets,10labGelsUUwithtext,8\labelstyle?,UU9L5ffA͉TU>'ExX2")Ʋ,UU2license,UU11lineUUbreak,5links,UU11loading,UU2merge,UU10movingUUtarget,6name,UU10newUUarrows,8\newdir?,UU8\NoCompileMatrices?,UU4o,UU5ob8ject,UU5\object?,UU8ob8jectUUmoGdi er,5,8,10\objectstyle?,UU9oldUUstyleofloading,11\OnlyOutlines?,UU4overwrite,UU6parallel,UU6\pit?,UU11plainUUtextentries,10pGoly*,UU12pGolygon-like,UU12pGosition,UU6ps,UU2quarterUUturn,7r,UU2radius,UU7relativeUUangle,7relativeUUentry*,6relativeUUvector,7repGeatUUlastob8ject,5retrievingUQXY U-pic,UU11gw:rotation,UU8,9 :round,UU10:roundUUshapGe,5:roundedUUframe,5:rows,UU2,6N8:segment,UU7:\SelectTips?{cm}{},UU8:shadedUUframe,5:shaft,UU5,8:shaftUUastip,6:shaftUUcharacters,8:shapGe,UU5:\ShowOutlines?,UU4:shrink,UU5:sideways,UU6:size,UU5:sliding,UU6:spacing,UU9:square,UU5:squigglyUUarrow,5:tail,UU5:target,UU6,10:targetUUentry*,2:text,UU5:textUUinentries,8:textUUlabGel,5:textUUstyle,2:tip,UU5,8:tipUUcharacters,8:tipUUinshaft,6:tripleUUarrow,5:turn,UU7:twoGcells,UU12:\txt?,UU5,8:u,UU2:uniformUUspacing,9:\usepackage?,UU2:v2,UU2:va(),UU7:vqariant,UU5,8:vector,UU6:vectorUUcoGordinates,7:vectorUUindirection,7:vectorUUtocorner,7:versionUU2,11:warranty*,UU11:web,UU12:W*orldUUWideWeb,11:x,UU5:\xymatrix?,UU2:\xymatrixnocompile?,UU4:\xyoption?,UU2,11:xypic.sty,UU11:xypic.tex,UU11LW916;l,t}\cmti7)- cmcsc10(- cmcsc10'N cmbx12&"V cmbx10% cmmi10 0ercmmi7O \cmmi5K`y cmr10ٓRcmr7Zcmr5u cmex10