; TeX output 1997.03.30:1237s\ȍ88GDtGGcmr17The7t߆TG cmtt12amscdpacqkage:XQ cmr12FVrankMittelbacrhRainerScrh opfJVMicrhaelDownes;28OctobSer1996 "VVersion1.02'&#"V cmbx1014?In9troQductionVu#K`y cmr10The'M S-TU>'ExXversion2.x(i.e.,simplerectangulardiagrams,#noUUdiagonalarrowsormoreexoticstu suppGorted). 2Example:"1" b> cmmi10S^ O!cmsy7WZcmr5Lȸ 8Tꍒ̐7 0ercmmi7j$kÍ>UM!ŵTu cmex10??y:6?:6?:6y8ٓRcmr7End wܴPLu(Sm 8Tc)=Ikffffffk(Z 8Tc)=Jo8(1)* 'ߤN cmtt9\begin{equation}\begin{CD} 'S^{{\mathcal{W}}_\Lambda}\otimesT,@>j>>T\\'@VVV@VV{\EndP}V\\'(S\otimesT)/IU @=Y(Z\otimesT)/J'\end{CD}\end{equation}#(assumingUU\Endisde nedasan`opGeratorname'.2AnotherUUexample:2W*eUUwillmakelibGeraluseofCichon'sDiagram[C8]:*ZVcove, (L)yl*>UM!lnon(K$)Cƍ>UM!jcf(K$)c ˍ>UM!.NAcf6_(L)at?at?atyx??=x=?=?6r?6r?6ryU'adde(L)yl*>UM!ladd(K$)Cƍ>UM!Ccov(K$)c ˍ>UM!*cnon: (L)o8(2))]'\begin{equation}\begin{CD}'\cov(\mathcal{L})@>>>\non(\mathcal{K})@>>>\cf(\mathcal{K})@>>>'\cf(\mathcal{L})\\'@VVV@AAA@AAA@VVV\\'\add(\mathcal{L})@>>>\add(\mathcal{K})@>>>\cov(\mathcal{K})@>>>'\non(\mathcal{L})'\end{CD}\end{equation}K1*s\ȍ8Y2|yp0J cmsl10THEUUAMSCDP*ACKAGE8GhStandardUUpackqageinfo. fc\NeedsTeXFormat{LaTeX2e}%LaTeX2.09can'tbeused(nornon-LaTeX) c[1994/12/01]%LaTeXdatemustDecember1994orlaterc\ProvidesPackage{amscd}[1996/10/28v1.2b]͍c\RequirePackage{amsgen}͍Y\math@crKshouldn'tbGede nedifitisalreadyde ned,MbecauseforCDKuseonly Ywe]wanttoomitthepartofthecoGderelatedto\dspbrk@lvl(seeamstex.sty).c\@ifundefined{math@cr}{%m\def\math@cr{{\ifnum0=`}\fiv\@ifstar{\global\@eqpen\@M\math@cr@}%{\global\@eqpen\interdisplaylinepenalty\math@cr@}}c}{}fYThefollowingsectionduplicatessomecoGdefromtheamstexpackqage,?incase Ythehamscdpackqageisusedbyitself.F*ordoGcumentationofthecoGderefertoYamstex.dtx.c\def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}} c\def\math@cr@@[#1]{\ifnum0=`{\fi}\math@cr@@@m\noalign{\vskip#1\relax}}c\def\restore@math@cr{\def\math@cr@@@{\cr}}c\restore@math@crc\def\rightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@m$#1\copy\z@\mkern-6mu\cleadersm\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfillm\mkern-6mu\mathord\rightarrow$}c\def\leftarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@m$#1\mathord\leftarrow\mkern-6mu\cleadersm\hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfillm\mkern-6mu\box\z@$}c\def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@m$#1\mathord\leftarrow\mkern-6mu\cleadersm\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfillm\mkern-6mu\mathord\rightarrow$}c\def\atdef@#1{\expandafter\def\csname\space@\string#1\endcsname}c\@ifundefined{Iat}{%m\DeclareRobustCommand{\Iat}{\FN@\at@}c}{}c\begingroup\catcode`\@=\activefYDe ne3Kmath@toreplicateitsmathcoGde-dictatedbehavior. Thisisincase@ YoGccursUUoutsideofCD.c\csnameif\string@compatibility\endcsnamec\else\fam=\mathcode`\@m\xdef@{\mathchar\number\fam\space}c\fic\gdef\CDat{\let@=\Iat}c\endgroupc\mathcode`\@="8000%make@pseudo-activeinmathc\def\at@{\let\next@\at@@ =s\ȍ8#1.INTRODUCTION38G2dD\ifcat\noexpand\nexta\else 2dD\ifcat\noexpand\next0\else2dD\ifcat\noexpand\next\relax\else2dD\let\next@\at@@@\fi\fi\fi\next@}-\def\at@@#1{\expandafter7\ifx\csname\space@\string#1\endcsname\relax@\DN@{\at@@@#1}%7\else@\DN@{\csname\space@\string#1\endcsname}%7\fi\next@}%#ThefollowingitemsshouldbGede nedonlyiftheyarenotalreadyde ned,either #toleavethepackqagenameuntouched(inthecaseof\PackageError)ortoavoid#redundantUUalloGcationoftokenordimenregisters. -\@ifundefined{default@tag}{% 7\def\default@tag{%@\def\tag{\PackageError{amscd}{\protect\tag\spacenotallowedJ2here}\@eha}}%-}{}%-\@ifundefined{at@@@}{%7\def\at@@@{\PackageError{amscd}{\Invalid@@@}{\the\athelp@}\char64\relax}-}{}-\@ifundefined{athelp@}{\csnamenewhelp\endcsname\athelp@-{Onlycertaincombinationsbeginningwith@makesensetome.^^J%-I'llassumeyouwanted@@foraprinted@.}}{}-\@ifundefined{minaw@}{\newdimen\minaw@}{}-\@ifundefined{bigaw@}{\newdimen\bigaw@}{}2Assignmentleofacoupleofdimensions,)andinitializationof\ampersand@. #W*eUUchecktoseeifweneedtode ne\minaw@and\bigaw@. -\minaw@11.111pt-\newdimen\minCDarrowwidth-\minCDarrowwidth2.5pc-\newif\ifCD@-\let\ampersand@\relax2Added%C\restore@math@cr\default@tagto xlinenumbGering%Cproblems,.7- #JUN-1991.qSuggestedUUbyI.Zakharevich. -\newenvironment{CD}{%7\CDat7\bgroup\relax\iffalse{\fi\let\ampersand@&\iffalse}\fi7\CD@true\vcenter\bgroup\let\\\math@cr\restore@math@cr\default@tag7\tabskip\z@skip\baselineskip20\ex@7\lineskip3\ex@\lineskiplimit3\ex@\halign\bgroup7&\hfill$\m@th##$\hfill\crcr-}{%7\crcr\egroup\egroup\egroup-}UU$\CD@check#This|pcheckisusedbyallmacrosthatmustnotappGearoutsidetheCD|fenviron-#ment.RThe rstargumentisthesymbGoltobeusedafter@,thesecondonetheˠs\ȍ8Y4|yTHEUUAMSCDP*ACKAGE8GYactionUUtobGeperformed. hOnce7againweusethetrickofde ningatempGorarycontrolsequence\next@Yand callingitafterthe nal\fi.uThisisnotabsolutelynecessary*,;butiten-YsuresqthattheconditionaltextisproGcessedinoneandthesamecolumnoftheYenclosingUUalignment. 鍑c\def\CD@check#1#2{\ifCD@\DN@{#2}\else m\DN@{\PackageError{amscd}{@\protect#1notvallowedoutsideoftheCDenvironment}\@eha}%m\fi\next@}躍c\atdef@>#1>#2>{\ampersand@m\ifCD@\global\bigaw@\minCDarrowwidth\else\global\bigaw@\minaw@\fim\setboxz@h{$\m@th\scriptstyle\;{#1}\;\;$}%m\ifdim\wdz@>\bigaw@\global\bigaw@\wdz@\fiEэYIfUU#2isemptywecansavesomework.m\@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%v\ifdim\wd\@ne>\bigaw@\global\bigaw@\wd\@ne\fi}%hdD\ifCD@\enskip\fiqp\mathrel{\mathop{\hboxto\bigaw@{\rightarrowfill@\displaystyle}}%{J\limits^{#1}\@ifnotempty{#2}{_{#2}}}%hdD\ifCD@\enskip\fi\ampersand@}c%c\atdef@<#1<#2<{\ampersand@m\ifCD@\global\bigaw@\minCDarrowwidth\else\global\bigaw@\minaw@\fim\setboxz@h{$\m@th\scriptstyle\;\;{#1}\;$}%m\ifdim\wdz@>\bigaw@\global\bigaw@\wdz@\fim\@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;\;{#2}\;$}%v\ifdim\wd\@ne>\bigaw@\global\bigaw@\wd\@ne\fi}%m\ifCD@\enskip\fiv\mathrel{\mathop{\hboxto\bigaw@{\leftarrowfill@\displaystyle}}%2\limits^{#1}\@ifnotempty{#2}{_{#2}}}%m\ifCD@\enskip\fi\ampersand@}鍑hV*ariants:oftheabGovetwoarrows,?using(and)charactersinsteadofUUcharacters,areprovidedforthosewhosekeybGoardsdon'thavethelatter.c\begingroup\catcode`\~=\active\lccode`\~=`\@c\lowercase{%m\global\atdef@)#1)#2){~>#1>#2>}m\global\atdef@(#1(#2({~<#1<#2<}c}%endlowercasec\endgroupEэc\atdef@A#1A#2A{\CD@check{A..A..A}{\llap{$\m@th\vcenter{\hboxm{$\scriptstyle#1$}}$}\Big\uparrowm\rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}c%c\atdef@V#1V#2V{\CD@check{V..V..V}{\llap{$\m@th\vcenter{\hboxm{$\scriptstyle#1$}}$}\Big\downarrowm\rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}c%s\ȍ8#1.INTRODUCTION58G-\atdef@={\CD@check={&\enskip\mathrel 7{\vbox{\hrule\@width\minCDarrowwidth\vskip2\ex@\hrule\@width7\minCDarrowwidth}}\enskip&}}-%-\atdef@|{\CD@check|{\Big\Vert&&}}-%-\atdef@\vert{\CD@check\vert{\Big\Vert&&}}-%-\atdef@.{\CD@check.{&&}}2The+\pretendcommandhasweirdsyntaxthatdoGesn't twellwithstandard #L5ffA͉TU>'ExXUUsyntaxsoweleaveitundone,atleastfornow.q[mjd,1994/10/27]-%\def\pretend#1\haswidth#2{\setboxz@h{$\m@th\scriptstyle{#2}$}\hbox-%to\wdz@{\hfill$\m@th\scriptstyle{#1}$\hfill}}2Theusual\endinputtoensurethatrandomgarbageattheendofthe le#doGesn'tUUgetcopiedbydocstrip.-\endinput';s\ p0J cmsl10ߤN cmtt9 cmmi10 0ercmmi7K`y cmr10ٓRcmr7Zcmr5u cmex10+d