\xycompiled{thesis-18}{2000/10/15:31 [thesis:405]}{Xy-pic 3.7}%
{\xymatrixnocompile { & T & T^{\vee }\ar [l]_{\vphi _a^{\vee }} & \coker (\vphi _a)^{\vee }\ar [l]\\ \ker (\vphi _t)^{\vee }& \Gamma \ar [l]\ar [u] &\Gamma ^{\vee }.\ar [l]^{\vphi _t^{\vee }}\ar [u] }}\relax 
\xy@{\xymatrix }{\enter@ {\def \noexpand \xy@minX@@ {\xy@minX@@ }\def \noexpand \xy@maxX@@ {\xy@maxX@@ }\def \noexpand \xy@minY@@ {\xy@minY@@ }\def \noexpand \xy@maxY@@ {\xy@maxY@@ }\edef \noexpand \xymatrixprefix@@ {\codeof \xymatrixprefix@@ }}}%
\xy@{}{\save@ \edef \matrixorigin@ {\X@c =\the \X@c \Y@c =\the \Y@c }\edef \xy@minX@@ {\the \X@c }\edef \xy@maxX@@ {\the \X@c }\edef \xy@minY@@ {\the \Y@c }\edef \xy@maxY@@ {\the \Y@c }}%
\xy@{""}{\edef \xymatrixprefix@@ {}}%
\xy@{}{\matrixorigin@ }%
\xy@{}{\L@c =3.0pt\R@c =3.0pt\D@c =3.0pt\U@c =3.0pt\Edge@c ={\rectangleEdge }\idfromc@ {1,1}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =8.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =23.02324pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =8.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =6.95987pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =23.02324pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =6.95987pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =6.95987pt\R@c =6.95988pt\D@c =6.74124pt\U@c =6.74124pt\Edge@c ={\rectangleEdge }\idfromc@ {1,2}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =8.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =6.95987pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =8.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =11.0261pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =6.95987pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =11.0261pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =10.04324pt\R@c =10.04326pt\D@c =7.20906pt\U@c =7.20906pt\Edge@c ={\rectangleEdge }\idfromc@ {1,3}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =8.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =11.0261pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =8.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =28.91676pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =11.0261pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =28.91676pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =28.91676pt\R@c =28.91678pt\D@c =8.5778pt\U@c =8.5778pt\Edge@c ={\rectangleEdge }\idfromc@ {1,4}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\cfromid@ {1,1}}%
\xy@{}{\dimen@ =8.5778pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =28.91676pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =8.5778pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =28.91676pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixrowsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@sinsign@@ \R@ }%
\xy@{}{\dimen@ =28.91676pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =28.91676pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixrowsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c -\xy@cossign@@ \R@ }%
\xy@{}{\L@c =23.02324pt\R@c =23.02324pt\D@c =8.5778pt\U@c =8.5778pt\Edge@c ={\rectangleEdge }\idfromc@ {2,1}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =8.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =23.02324pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =8.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =6.95987pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =23.02324pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =6.95987pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =6.42188pt\R@c =6.42189pt\D@c =6.74124pt\U@c =6.74124pt\Edge@c ={\rectangleEdge }\idfromc@ {2,2}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =8.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =6.95987pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =8.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =11.0261pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =6.95987pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =11.0261pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =8.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =11.0261pt\R@c =11.0261pt\D@c =7.20906pt\U@c =7.20906pt\Edge@c ={\rectangleEdge }\idfromc@ {2,3}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\ifx \xymatrixsavedCOORD@ \relax \enter@ {\noexpand \let \noexpand \COORD@ \noexpand \xymatrixsavedCOORD@ }\let \xymatrixsavedCOORD@ =\COORD@ \let \COORD@ =\xymatrixCOORD@ \else \enter@ {}\fi }%
\xy@{ENTRY "1,1"}{\Row =1 \Col =1\relax \cfromid@ {1,1}\pfromc@ }%
\xy@@ix@{{\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "1,2"}{\Row =1 \Col =2\relax \cfromid@ {1,2}\pfromc@ }%
\xy@@ix@{{\entrybox }{T }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "1,3"}{\Row =1 \Col =3\relax \cfromid@ {1,3}\pfromc@ }%
\xy@@ix@{{\entrybox }{T^{\vee }\ar [l]_{\vphi _a^{\vee }} }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[l]}{\def \thematrixCOORD@@ {[l]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,2\endcsname \ifx \next@ \relax \xyerror@RC {1,2}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{}}\relax 
\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{_}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@{}{\enter@ \DirectionfromtheDirection@ }%
\xy@@ix@{\labelbox {\vphi _a^{\vee }}}\relax 
\xy@{}{\setbox \z@ =\expandafter \object \the \toks 9 \advance \L@c \labelmargin@ \advance \R@c \labelmargin@ \advance \D@c \labelmargin@ \advance \U@c \labelmargin@ \setboxz@h {\kern \labelmargin@ \boxz@ \kern \labelmargin@ }\A@ =\X@c \B@ =\Y@c \aboveDirection@ \xydashl@ \the \Edge@c \thr@@ \advance \A@ -\X@c \advance \B@ -\Y@c \advance \X@c 2\A@ \advance \Y@c 2\B@ \ht \z@ =\U@c \dp \z@ =\D@c \dimen@ =\L@c \advance \dimen@ \R@c \wd \z@ =\dimen@ \setbox \lastobjectbox@ =\hbox {\X@c =\L@c \Y@c =\z@ \Drop@@ }\drop@ {\box \lastobjectbox@ }{}\leave@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{ENTRY "1,4"}{\Row =1 \Col =4\relax \cfromid@ {1,4}\pfromc@ }%
\xy@@ix@{{\entrybox }{\protect \coker  (\vphi _a)^{\vee }\ar [l]}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[l]}{\def \thematrixCOORD@@ {[l]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,3\endcsname \ifx \next@ \relax \xyerror@RC {1,3}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{}}\relax 
\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{ENTRY "2,1"}{\Row =2 \Col =1\relax \cfromid@ {2,1}\pfromc@ }%
\xy@@ix@{{\entrybox }{\protect \qopname  \relax o{ker}(\vphi _t)^{\vee }}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "2,2"}{\Row =2 \Col =2\relax \cfromid@ {2,2}\pfromc@ }%
\xy@@ix@{{\entrybox }{\Gamma \ar [l]\ar [u] }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[l]}{\def \thematrixCOORD@@ {[l]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,1\endcsname \ifx \next@ \relax \xyerror@RC {2,1}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{}}\relax 
\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[u]}{\def \thematrixCOORD@@ {[u]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,2\endcsname \ifx \next@ \relax \xyerror@RC {1,2}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{}}\relax 
\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{ENTRY "2,3"}{\Row =2 \Col =3\relax \cfromid@ {2,3}\pfromc@ }%
\xy@@ix@{{\entrybox }{\Gamma ^{\vee }.\ar [l]^{\vphi _t^{\vee }}\ar [u] }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[l]}{\def \thematrixCOORD@@ {[l]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,2\endcsname \ifx \next@ \relax \xyerror@RC {2,2}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{}}\relax 
\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{^}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@{}{\enter@ \DirectionfromtheDirection@ }%
\xy@@ix@{\labelbox {\vphi _t^{\vee }}}\relax 
\xy@{}{\setbox \z@ =\expandafter \object \the \toks 9 \advance \L@c \labelmargin@ \advance \R@c \labelmargin@ \advance \D@c \labelmargin@ \advance \U@c \labelmargin@ \setboxz@h {\kern \labelmargin@ \boxz@ \kern \labelmargin@ }\A@ =\X@c \B@ =\Y@c \belowDirection@ \xydashl@ \the \Edge@c \thr@@ \advance \A@ -\X@c \advance \B@ -\Y@c \advance \X@c 2\A@ \advance \Y@c 2\B@ \ht \z@ =\U@c \dp \z@ =\D@c \dimen@ =\L@c \advance \dimen@ \R@c \wd \z@ =\dimen@ \setbox \lastobjectbox@ =\hbox {\X@c =\L@c \Y@c =\z@ \Drop@@ }\drop@ {\box \lastobjectbox@ }{}\leave@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[u]}{\def \thematrixCOORD@@ {[u]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,3\endcsname \ifx \next@ \relax \xyerror@RC {1,3}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{}}\relax 
\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{}{\leave@ }%
\xy@{}{}%
\xy@{\restore }{\leave@ }%
\xy@{}{\edef \nextii@ {{\xy@minX@@ }{\xy@maxX@@ }{\xy@minY@@ }{\xy@maxY@@ }}\expandafter \xymatrix@insert@ \nextii@ }%
\xy@{}{\leave@ }%
\xyendcompiled