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\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 }{X_J\ar [r]\ar @{=}[d]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \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@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {=}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir 2{}}}{}% \xy@{~>{|>*h\dir 2{}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \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 2}{}}\relax \xy@{\drop !Ch\dir 2{}}{\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 2}{}}\relax \xy@{\drop !Ch\dir 2{}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "1,2"}{\Row =1 \Col =2\relax \cfromid@ {1,2}\pfromc@ }% \xy@@ix@{{\entrybox }{\protect \Hom (X_J,\Z )\ar [r]\ar [d]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \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@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \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@{>}{\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 "1,3"}{\Row =1 \Col =3\relax \cfromid@ {1,3}\pfromc@ }% \xy@@ix@{{\entrybox }{\Phi _J \ar [r]\ar [d]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,4\endcsname \ifx \next@ \relax \xyerror@RC {1,4}\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,3\endcsname \ifx \next@ \relax \xyerror@RC {2,3}\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 "1,4"}{\Row =1 \Col =4\relax \cfromid@ {1,4}\pfromc@ }% \xy@@ix@{{\entrybox }{0}}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{ENTRY "2,1"}{\Row =2 \Col =1\relax \cfromid@ {2,1}\pfromc@ }% \xy@@ix@{{\entrybox }{X_J\ar [r]\ar @{=}[d]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \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@{>}{\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 2{}}}{}% \xy@{~>{|>*h\dir 2{}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,1\endcsname \ifx \next@ \relax \xyerror@RC {3,1}\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 2}{}}\relax \xy@{\drop !Ch\dir 2{}}{\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 2}{}}\relax \xy@{\drop !Ch\dir 2{}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "2,2"}{\Row =2 \Col =2\relax \cfromid@ {2,2}\pfromc@ }% \xy@@ix@{{\entrybox }{\protect \Hom (\cL ,\Z )\ar [r]\ar [d]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,3\endcsname \ifx \next@ \relax \xyerror@RC {2,3}\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@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,2\endcsname \ifx \next@ \relax \xyerror@RC {3,2}\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 }{\Phi _\cL \ar [r]\ar [d] }}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,4\endcsname \ifx \next@ \relax \xyerror@RC {2,4}\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,3\endcsname \ifx \next@ \relax \xyerror@RC {3,3}\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 "2,4"}{\Row =2 \Col =4\relax \cfromid@ {2,4}\pfromc@ }% \xy@@ix@{{\entrybox }{0}}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{ENTRY "3,1"}{\Row =3 \Col =1\relax \cfromid@ {3,1}\pfromc@ }% \xy@@ix@{{\entrybox }{X_J\ar [r]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,2\endcsname \ifx \next@ \relax \xyerror@RC {3,2}\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 "3,2"}{\Row =3 \Col =2\relax \cfromid@ {3,2}\pfromc@ }% \xy@@ix@{{\entrybox }{\protect \Hom (\pi ^*X_A,\Z )\ar [r]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,3\endcsname \ifx \next@ \relax \xyerror@RC {3,3}\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 "3,3"}{\Row =3 \Col =3\relax \cfromid@ {3,3}\pfromc@ }% \xy@@ix@{{\entrybox }{\Phi _A \ar [r]}}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,4\endcsname \ifx \next@ \relax \xyerror@RC {3,4}\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 "3,4"}{\Row =3 \Col =4\relax \cfromid@ {3,4}\pfromc@ }% \xy@@ix@{{\entrybox }{0. }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{}{\leave@ }% \xy@{}{}% \xy@{\restore }{\leave@ }% \xy@{}{\edef \nextii@ {{\xy@minX@@ }{\xy@maxX@@ }{\xy@minY@@ }{\xy@maxY@@ }}\expandafter \xymatrix@insert@ \nextii@ }% \xy@{}{\leave@ }% \xyendcompiled