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蛇形引理和使连接态射通过其他引理

tag-icon • tag-icon tikz-cd commutative-diagrams
蛇形引理和使连接态射通过其他引理

我正在尝试绘制蛇形引理图，但连接态射没有像我希望的那样从其他态射下方通过（它确实从下方通过，但间距不够，第二张图应该能清楚地说明我的意思），而且我也想移动它的标签，就像第二张图一样。

蛇形稃

蛇形引理 我想要它

\[\begin{tikzcd}
{} & \red{\ker f'} \arrow[r, "\overline{\alpha}", red] \arrow[d, hook, "i'"] & \red{\ker f} \arrow[r, "\overline{\beta}", red] \arrow[d, hook, "i"] & \red{\ker f''} \arrow[d, hook, "i''"] 
\arrow[ddd, phantom, ""{coordinate, name=Z}] \arrow[dddll,
    "\delta",
    rounded corners,
    to path={ -- ([xshift=2ex]\tikztostart.east)
              |- (Z) [near end]\tikztonodes
              -| ([xshift=-2ex]\tikztotarget.west)
              -- (\tikztotarget)}, red] & {}\\
{} & M' \arrow[r, "\alpha"] \arrow[d, "f'"] & M \arrow[r, "\beta"] \arrow[d, "f"] & M'' \arrow[r] \arrow[d, "f''"] & 0 \\
0 \arrow[r] & N' \arrow[r, "\alpha'"] \arrow[d, two heads, "\pi'"] & N \arrow[r, "\beta'"] \arrow[d, two heads, "\pi"] & N'' \arrow[d, two heads, "\pi''"] & {} \\
{} & \red{\coker f'} \arrow[r, "\overline{\alpha'}", red] & \red{\coker f} \arrow[r, "\overline{\beta'}", red] & \red{\coker f''} & {}
\end{tikzcd}\]

答案1

你需要找到一种方法来告诉 tikzcd，f、f'、f'' 带有白色背景。例如 \def\atfield[#1]{\arrow[#1,nodes={fill=white}]}

您还可以使用它preaction={draw=white,-,line width=3} 来为箭头创建白色背景。

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}

\def\red#1{|[red]|#1}
\def\coker{\operatorname{coker}}
\def\atfield[#1]{\arrow[#1,preaction={draw=white,-,line width=3},nodes={fill=white}]}

\[\begin{tikzcd}
{} & \red{\ker f'} \arrow[r, "\overline{\alpha}", red] \arrow[d, hook, "i'"] & \red{\ker f} \arrow[r, "\overline{\beta}", red] \arrow[d, hook, "i"] & \red{\ker f''} \arrow[d, hook, "i''"] 
\arrow[ddd, phantom, ""{coordinate, name=Z}] \arrow[dddll,
    "\qquad\delta",
    rounded corners,
    to path={ -- ([xshift=2ex]\tikztostart.east)
              |- (Z) [near end]\tikztonodes
              -| ([xshift=-2ex]\tikztotarget.west)
              -- (\tikztotarget)}, red] & {}\\
{} & M' \arrow[r, "\alpha"] \atfield[d, "f'"] & M \arrow[r, "\beta"] \atfield[d, "f"] & M'' \arrow[r] \atfield[d, "f''"] & 0 \\
0 \arrow[r] & N' \arrow[r, "\alpha'"] \arrow[d, two heads, "\pi'"] & N \arrow[r, "\beta'"] \arrow[d, two heads, "\pi"] & N'' \arrow[d, two heads, "\pi''"] & {} \\
{} & \red{\coker f'} \arrow[r, "\overline{\alpha'}", red] & \red{\coker f} \arrow[r, "\overline{\beta'}", red] & \red{\coker f''} & {}
\end{tikzcd}\]

\end{document}

答案2

这不使用tikz-cd，但基于给出的答案如何绘制蛇形引理中连接同态的“蛇”形箭头？。间隙的大小部分是硬编码的，因为它们必须包含节点和边缘。我还没有将其调整到您的标签，但这应该是直截了当的（我建议使用节点，asymmetrical rectangle以便alpha和beta标签水平对齐）。

\documentclass[border=10]{standalone}
%\url{https://tex.stackexchange.com/q/611629/86}
\thispagestyle{empty}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{tikz-cd}
\usetikzlibrary{%
  matrix,%
  calc,%
  arrows%
}

\DeclareMathOperator{\coker}{coker}

\begin{document}
\begin{tikzpicture}[>=triangle 60]
\matrix[matrix of math nodes,column sep={60pt,between origins},row sep={60pt,between origins},nodes={asymmetrical rectangle}] (s)
{
&|[name=ka]| \ker f &|[name=kb]| \ker g &|[name=kc]| \ker h \\
%
&|[name=A]| A' &|[name=B]| B' &|[name=C]| C' &|[name=01]| 0 \\
%
|[name=02]| 0 &|[name=A']| A &|[name=B']| B &|[name=C']| C \\
%
&|[name=ca]| \coker f &|[name=cb]| \coker g &|[name=cc]| \coker h \\
};
\draw[->] (ka) edge (A)
          (kb) edge (B)
          (kc) edge (C)
          (A) edge (B)
          (B) edge node[auto] {\(p\)} (C)
          (C) edge (01)
          (A) edge node[auto,asymmetrical rectangle] (f) {\(f\)} (A')
          (B) edge node[auto,asymmetrical rectangle] (g) {\(g\)} (B')
          (C) edge node[auto,asymmetrical rectangle] (h) {\(h\)} (C')
          (02) edge (A')
          (A') edge node[auto] {\(i\)} (B')
          (B') edge (C')
          (A') edge (ca)
          (B') edge (cb)
          (C') edge (cc)
;
\draw[->,gray] (ka) edge (kb)
               (kb) edge (kc)
               (ca) edge (cb)
               (cb) edge (cc)
;
\draw[->,gray,rounded corners] (kc) -| node[auto,text=black,pos=.7] {\(\partial\)} ($(01.east)+(.5,0)$)  |-
(h.mid east) (h.mid west) +(-.1,0) --
(g.mid east) (g.mid west) +(-.1,0) --
(f.mid east) (f.mid west) +(-.1,0)
 -| ($(02.west)+(-.5,0)$) |- (ca);

\end{tikzpicture}
\end{document}

有间隙的蛇形稃

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