Box several arrows in different levels

Question

So I've drawn this diagram

 \begin{tikzcd}
 & & & 0 &  \\

0\arrow[r] & \ker{d^i}\arrow[d]\arrow[r] &
 A^i\arrow[d]\arrow[r] & \Ima{d^{i-1}}\arrow[r]\arrow[u] & 0\\

0 \arrow[r] &  H^i(A^*)\arrow[r] & A^i/ \Ima{d^{i-1}}\arrow[ur] & & 
\end{tikzcd}

I'd like to box the short exact sequence that is curved, in order to get something like this (which I made with Paint)

Is there any non-extremely complicated way to do this? I don't mind if the solution implies using tikzpicture or something instead of tikzcd.

Answer 1

It is certainly possible using the methods of this answer, i.e. by remembering the nodes and placing an overlay.

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{amsmath}
\DeclareMathOperator*{\im}{Im}
\begin{document}
\[
\begin{tikzcd}[remember picture] % see https://tex.stackexchange.com/a/256562/121799
 & & & 0 &  \\
0\arrow[r] & \ker{d^i}\arrow[d]\arrow[r] &
 A^i\arrow[d]\arrow[r] & \im a{d^{i-1}}\arrow[r]\arrow[u] & 0\\
0 \arrow[r] &  H^i(A^*)\arrow[r] & A^i/ \im a{d^{i-1}}\arrow[ur] & & 
\end{tikzcd}
\]
\tikz[remember picture,overlay]{
\draw[-] (tikz@f@1-3-1.south west|-tikz@f@1-3-3.south east)
--(tikz@f@1-3-1.north west|-tikz@f@1-3-3.north)
--(tikz@f@1-3-3.north) --(tikz@f@1-2-4.west)
--(tikz@f@1-2-4.west|-tikz@f@1-1-4.north west)
--(tikz@f@1-2-4.south east|-tikz@f@1-1-4.north east)
--(tikz@f@1-2-4.south east)
--(tikz@f@1-3-3.south east)--cycle;
}
\end{document}

As you see, the contour tends to interfere with the arrows. One can cure this by adding some small shifts here and there. But I'd like to argue that an even better way of highlighting the contour is to shade it.

\documentclass{article}
\usepackage{tikz-cd}
\usepackage{amsmath}
\DeclareMathOperator{\Ima}{Im}
\begin{document}
\[
\begin{tikzcd}[remember picture] % see https://tex.stackexchange.com/a/256562/121799
 & & & 0 &  \\
0\arrow[r] & \ker{d^i}\arrow[d]\arrow[r] &
 A^i\arrow[d]\arrow[r] & \Ima a{d^{i-1}}\arrow[r]\arrow[u] & 0\\
0 \arrow[r] &  H^i(A^*)\arrow[r] & A^i/ \Ima a{d^{i-1}}\arrow[ur] & & 
\end{tikzcd}
\]
\tikz[remember picture,overlay]{
\fill[blue,opacity=0.2] (\tikzcdmatrixname-3-1.south west|-\tikzcdmatrixname-3-3.south east)
--(\tikzcdmatrixname-3-1.north west|-\tikzcdmatrixname-3-3.north)
--(\tikzcdmatrixname-3-3.north) --(\tikzcdmatrixname-2-4.west)
--(\tikzcdmatrixname-2-4.west|-\tikzcdmatrixname-1-4.north west)
--(\tikzcdmatrixname-2-4.south east|-\tikzcdmatrixname-1-4.north east)
--(\tikzcdmatrixname-2-4.south east)
--(\tikzcdmatrixname-3-3.south east)--cycle;
}

\[
\begin{tikzcd}[remember picture] % see https://tex.stackexchange.com/a/256562/121799
 & & & 0 &  \\
0\arrow[r] & \ker{d^i}\arrow[d]\arrow[r] &
 A^i\arrow[d]\arrow[r] & \Ima a{d^{i-1}}\arrow[r]\arrow[u] & 0\\
0 \arrow[r] &  H^i(A^*)\arrow[r] & A^i/ \Ima a{d^{i-1}}\arrow[ur] & & 
\end{tikzcd}
\]
\tikz[remember picture,overlay]{
\fill[red,opacity=0.2] (\tikzcdmatrixname-3-1.south west|-\tikzcdmatrixname-3-3.south east)
--(\tikzcdmatrixname-3-1.north west|-\tikzcdmatrixname-3-3.north)
--(\tikzcdmatrixname-3-3.north) --(\tikzcdmatrixname-2-4.west)
--(\tikzcdmatrixname-2-4.west|-\tikzcdmatrixname-1-4.north west)
--(\tikzcdmatrixname-2-4.south east|-\tikzcdmatrixname-1-4.north east)
--(\tikzcdmatrixname-2-4.south east)
--(\tikzcdmatrixname-3-3.south east)--cycle;
}
\end{document}

In this case, you do not have to mess around with these shifts.

NOTE: In the first snippet, the first number, 1, in tikz@f@1-3-3 (say) refers to the diagram. If you have more than one commutative diagrams (as in the second snippet), one needs to to take care that. I didn't find a documentation on that, but in tikzlibrarycd.code.tex one finds

\def\tikzcd@ar@target{\tikzcdmatrixname-\tikzcd@currentrow-\tikzcd@currentcolumn} 

And this seems to do the trick.