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Diffstat (limited to 'buch/chapters/95-homologie/komplex.tex')
-rw-r--r-- | buch/chapters/95-homologie/komplex.tex | 36 |
1 files changed, 19 insertions, 17 deletions
diff --git a/buch/chapters/95-homologie/komplex.tex b/buch/chapters/95-homologie/komplex.tex index fa2d8e1..9787bb2 100644 --- a/buch/chapters/95-homologie/komplex.tex +++ b/buch/chapters/95-homologie/komplex.tex @@ -56,7 +56,7 @@ für jedes $k$ \circ f_{k} = -f_{k+1} +f_{k-1} \circ \partial^C_k \label{buch:komplex:abbildung} @@ -69,31 +69,33 @@ kommutatives Diagramm dargestellt werden. \begin{equation} \begin{tikzcd} 0 - & C_0 \arrow[l, "\partial_0^C"] + & C_0 \arrow[l, "\partial_0^C" above] \arrow[d, "f_0"] - & C_1 \arrow[l,"\partial_1^C"] + & C_1 \arrow[l,"\partial_1^C" above] \arrow[d, "f_1"] - & C_2 \arrow[l,"\partial_2^C"] + & C_2 \arrow[l,"\partial_2^C" above] \arrow[d, "f_2"] & \dots \arrow[l] - \arrow[l, "\partial_{k-1}^C"] - & C_k - \arrow[l, "\partial_k^C"] - \arrow[d, "f_k"] - & C_{k+1}\arrow[l, "\partial_{k+1}^C"] - \arrow[d, "f_{k+1}"] + \arrow[l, "\partial_{3}^C" above] + & C_{k-1} + \arrow[l, "\partial_{k-1}^C" above] + \arrow[d, "f_{k-1}"] + & C_{k}\arrow[l, "\partial_{k}^C" above] + \arrow[d, "f_{k}"] & \dots + \arrow[l,"\partial_{k+1}^C" above] \\ 0 - & D_0 \arrow[l, "\partial_0^D"] - & D_1 \arrow[l,"\partial_1^D"] - & D_2 \arrow[l,"\partial_2^D"] + & D_0 \arrow[l, "\partial_0^D" above] + & D_1 \arrow[l,"\partial_1^D" above] + & D_2 \arrow[l,"\partial_2^D" above] & \dots \arrow[l] - \arrow[l, "\partial_{k-1}^D"] - & D_k - \arrow[l, "\partial_k^D"] - & D_{k+1}\arrow[l, "\partial_{k+1}^D"] + \arrow[l, "\partial_{3}^D" above] + & D_{k-1} + \arrow[l, "\partial_{k-1}^D" above] + & D_{k}\arrow[l, "\partial_{k}^D" above] & \dots + \arrow[l,"\partial_{k+1}^D" above] \end{tikzcd} \label{buch:komplex:abbcd} \end{equation} |