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\R@ }% \xy@{}{\dimen@ =37.19489pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =9.65376pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =29.01382pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =9.65376pt\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 =5.7375pt\R@c =5.7375pt\D@c =6.52832pt\U@c =6.52832pt\Edge@c ={\rectangleEdge }\idfromc@ {5,2}}% \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@ =9.65376pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =29.01382pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =9.65376pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =37.49905pt\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@ =29.01382pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =9.65376pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =37.49905pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =9.65376pt\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 =5.7375pt\R@c =5.7375pt\D@c =6.52832pt\U@c =6.52832pt\Edge@c ={\rectangleEdge }\idfromc@ {5,3}}% \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 }{0\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@{[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 }{}}\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 "1,2"}{\Row =1 \Col =2\relax \cfromid@ {1,2}\pfromc@ }% \xy@@ix@{{\entrybox }{0\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@{[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 }{0\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@{[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 "2,1"}{\Row =2 \Col =1\relax \cfromid@ {2,1}\pfromc@ }% \xy@@ix@{{\entrybox }{H[I_f]\ar [d]\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@{[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 }{}}\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@{[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@{ENTRY "2,2"}{\Row =2 \Col =2\relax \cfromid@ {2,2}\pfromc@ }% \xy@@ix@{{\entrybox }{H\ar [d]\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@{[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@{\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@{ENTRY "2,3"}{\Row =2 \Col =3\relax \cfromid@ {2,3}\pfromc@ }% \xy@@ix@{{\entrybox }{\Phi _f(H)\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@{[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 "3,1"}{\Row =3 \Col =1\relax \cfromid@ {3,1}\pfromc@ }% \xy@@ix@{{\entrybox }{\protect \Hom (S,\C )[I_f]\ar [d]\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,1\endcsname \ifx \next@ \relax \xyerror@RC {4,1}\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@{[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 (S,\C )\ar [d]\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,2\endcsname \ifx \next@ \relax \xyerror@RC {4,2}\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 {}}}{}% \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 }{\protect \Hom (S[I_f],\C )\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,3\endcsname \ifx \next@ \relax \xyerror@RC {4,3}\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 "4,1"}{\Row =4 \Col =1\relax \cfromid@ {4,1}\pfromc@ }% \xy@@ix@{{\entrybox }{{A_f^{\vee }(\C )}\ar [d]\ar [r] \ar @/_3.5pc/[rr]}}\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@5,1\endcsname \ifx \next@ \relax \xyerror@RC {5,1}\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@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,2\endcsname \ifx \next@ \relax \xyerror@RC {4,2}\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@{~={\save @(,\xy@ {**{} ?+/_3.5pc/+/_3.5pc/ @+c}{\setupDirection@ \vfromslide@ {_3.5pc}\X@c =2\X@c \advance \X@c \X@p \advance \X@c .5\d@X \Y@c =2\Y@c \advance \Y@c \Y@p \advance \Y@c .5\d@Y \czeroEdge@ \spushc@ }\restore \preconnect \crvi {-}}}{}% \xy@{~/{\POS @i @) }}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[rr]}{\def \thematrixCOORD@@ {[rr]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,3\endcsname \ifx \next@ \relax \xyerror@RC {4,3}\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={\save @(,\xy@ {**{} ?+/_3.5pc/+/_3.5pc/ @+c}{\setupDirection@ \vfromslide@ {_3.5pc}\X@c =2\X@c \advance \X@c \X@p \advance \X@c .5\d@X \Y@c =2\Y@c \advance \Y@c \Y@p \advance \Y@c .5\d@Y \czeroEdge@ \spushc@ }\restore \preconnect \crvi {-}}}{}% \xy@{\save }{\save@ }% \xy@{@(}{\senter@ }% \xy@{,}{\comma@@ }% \xy@{**{} ?+/_3.5pc/+/_3.5pc/ @+c}{\setupDirection@ \vfromslide@ {_3.5pc}\X@c =2\X@c \advance \X@c \X@p \advance \X@c .5\d@X \Y@c =2\Y@c \advance \Y@c \Y@p \advance \Y@c .5\d@Y \czeroEdge@ \spushc@ }% \xy@{\restore }{\leave@ }% \xy@@ix@{{\crvi }{-}}\relax \xy@{\connect \crvi {-}}{\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/{\POS @i @) }}{}% \xy@{@i}{\sinit@ }% \xy@{@)}{\sleave@ }% \xy@{\restore }{\leave@ }% \xy@{ENTRY "4,2"}{\Row =4 \Col =2\relax \cfromid@ {4,2}\pfromc@ }% \xy@@ix@{{\entrybox }{J_0(N)(\C )\ar [d]\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@5,2\endcsname \ifx \next@ \relax \xyerror@RC {5,2}\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 {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,3\endcsname \ifx \next@ \relax \xyerror@RC {4,3}\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 "4,3"}{\Row =4 \Col =3\relax \cfromid@ {4,3}\pfromc@ }% \xy@@ix@{{\entrybox }{A_f(\C )\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@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@5,3\endcsname \ifx \next@ \relax \xyerror@RC {5,3}\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 "5,1"}{\Row =5 \Col =1\relax \cfromid@ {5,1}\pfromc@ }% \xy@@ix@{{\entrybox }{0 }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{ENTRY "5,2"}{\Row =5 \Col =2\relax \cfromid@ {5,2}\pfromc@ }% \xy@@ix@{{\entrybox }{0 }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{ENTRY "5,3"}{\Row =5 \Col =3\relax \cfromid@ {5,3}\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