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{\xymatrixnocompile { & 0 \ar [rr] & & A^p \ar @{^{(}->}[rr]^{f^p} \ar [ld]_{d_A^p} \ar '[d][dd]^{\alpha ^p} & & B^p \ar @{>>}[rr]^{g^p} \ar [ld]_{d_B^p} \ar @/^/@{.>}[ld] \ar '[d][dd]^{\beta ^p} & & C^p \ar [rr] \ar [ld]_{d_C^p} \ar @/^/@{.>}[ll] \ar '[d][dd]^{\gamma ^p} \ar @/_/@{.>}[dd] & & 0 \\ 0 \ar [rr] & & A^{p+1} \ar @{^{(}->}[rr]^(.7){f^{p+1}} \ar [dd]^(.3){\alpha ^{p+1}} \ar @/_/@{.>}[dd] & & B^{p+1} \ar @{>>}[rr]^(.7){g^{p+1}} \ar @/^/@{.>}[ll] \ar [dd]^(.3){\beta ^{p+1}} & & C^{p+1} \ar [rr] \ar [dd]^(.3){\gamma ^{p+1}} & & 0 & \\ & 0 \ar '[r][rr] & & A_1^p \ar [ld]_{d_{A_{1}}^p} \ar @{^{(}->}'[r]^{f_1^{p}}[rr] & & B_1^p \ar [ld]_{d_{B_1}^p} \ar @{>>}'[r]^{g_1^{p}}[rr] \ar @/^/@{.>}[ld] & & C_1^p \ar [rr] \ar [ld]_{d_{C_1}^p} \ar @/^/@{.>}[ll] & & 0 \\ 0 \ar [rr] & & A_1^{p+1} \ar @{^{(}->}[rr]^{f_1^{p+1}} & & B_1^{p+1} \ar @{>>}[rr]^{g_1^{p+1}} \ar @/^/@{.>}[ll] & & C_1^{p+1} \ar [rr] & & 0 & }}\relax 
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\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@ }%
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\xy@{\save }{\save@ }%
\xy@{@(}{\senter@ }%
\xy@{,}{\comma@@ }%
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\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@@ }%
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\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
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\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
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\xy@{@i}{\sinit@ }%
\xy@{@)}{\sleave@ }%
\xy@{\restore }{\leave@ }%
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\xy@@ix@{{!V\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "3,8"}{\Row =3 \Col =8\relax \cfromid@ {3,8}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{C_1^p \ar [rr] \ar [ld]_{d_{C_1}^p} \ar @/^/@{.>}[ll] }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
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\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[rr]}{\def \thematrixCOORD@@ {[rr]}}%
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\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@ }%
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\xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
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\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@ }%
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\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
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\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
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\xy@{~/{}}{}%
\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[ld]}{\def \thematrixCOORD@@ {[ld]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,7\endcsname \ifx \next@ \relax \xyerror@RC {4,7}\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 {d_{C_1}^p}}\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@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\save @(,\xy@ {**{} ?+/^/+/^/ @+c}{\setupDirection@ \vfromslide@ {^}\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 {.}}}{}%
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\xy@{~<{|<*h\dir {}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[ll]}{\def \thematrixCOORD@@ {[ll]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,6\endcsname \ifx \next@ \relax \xyerror@RC {3,6}\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@ {**{} ?+/^/+/^/ @+c}{\setupDirection@ \vfromslide@ {^}\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@{**{} ?+/^/+/^/ @+c}{\setupDirection@ \vfromslide@ {^}\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 "3,9"}{\Row =3 \Col =9\relax \cfromid@ {3,9}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "3,10"}{\Row =3 \Col =10\relax \cfromid@ {3,10}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{0 }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "4,1"}{\Row =4 \Col =1\relax \cfromid@ {4,1}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{0 \ar [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@{[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={\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 "4,2"}{\Row =4 \Col =2\relax \cfromid@ {4,2}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "4,3"}{\Row =4 \Col =3\relax \cfromid@ {4,3}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{A_1^{p+1} \ar @{^{(}->}[rr]^{f_1^{p+1}} }}\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@{[rr]}{\def \thematrixCOORD@@ {[rr]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,5\endcsname \ifx \next@ \relax \xyerror@RC {4,5}\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 {f_1^{p+1}}}\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@{ENTRY "4,4"}{\Row =4 \Col =4\relax \cfromid@ {4,4}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "4,5"}{\Row =4 \Col =5\relax \cfromid@ {4,5}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{B_1^{p+1} \ar @{>>}[rr]^{g_1^{p+1}} \ar @/^/@{.>}[ll] }}\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@{[rr]}{\def \thematrixCOORD@@ {[rr]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,7\endcsname \ifx \next@ \relax \xyerror@RC {4,7}\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 {g_1^{p+1}}}\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@{~={\save @(,\xy@ {**{} ?+/^/+/^/ @+c}{\setupDirection@ \vfromslide@ {^}\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@{[ll]}{\def \thematrixCOORD@@ {[ll]}}%
\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@ {**{} ?+/^/+/^/ @+c}{\setupDirection@ \vfromslide@ {^}\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@{**{} ?+/^/+/^/ @+c}{\setupDirection@ \vfromslide@ {^}\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 "4,6"}{\Row =4 \Col =6\relax \cfromid@ {4,6}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "4,7"}{\Row =4 \Col =7\relax \cfromid@ {4,7}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{C_1^{p+1} \ar [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@{[rr]}{\def \thematrixCOORD@@ {[rr]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@4,9\endcsname \ifx \next@ \relax \xyerror@RC {4,9}\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 "4,8"}{\Row =4 \Col =8\relax \cfromid@ {4,8}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "4,9"}{\Row =4 \Col =9\relax \cfromid@ {4,9}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{0 }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "4,10"}{\Row =4 \Col =10\relax \cfromid@ {4,10}\pfromc@ }%
\xy@@ix@{{!V\entrybox }{}}\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