# How to group objects in parallelogram?

How to group the blue objects $C_{n+1},C_n,D_{n+1},D_n$ in my codes in a parallelogram just like the following picture using the command '\save' ?

\documentclass{article}
\usepackage[all]{xy}
\begin{document}
$$\xymatrix{ C:\ar[dd]_{\varphi}^{\psi} & \cdots\ar[r] & C_{n+1}\ar[rr]^{\partial_{n+1}^C}\ar[dd] && C_n\ar[rr]^{\partial_n^C}\ar[dd]_{\varphi_n}^{\psi_n}\ar[ddll]_{T_n} && C_{n-1}\ar[ddll]_{T_{n-1}}\ar[r]\ar[dd] & \cdots\\\\ D: & \cdots\ar[r] & D_{n+1}\ar[rr]^{\partial_{n+1}^D} && D_n\ar[rr]^{\partial_n^D} && D_{n-1}\ar[r] & \cdots,}$$
\end{document}


What I need is grouping the following blue objects:

Not exactly the same diagram, and not exactly a parallelogram, but here's something similar using the tikz-cd package:
\documentclass{article}
$\begin{tikzcd} C:\ar[dd,"\varphi"',"\psi"] & \cdots\ar[r] & C_{n+1}\ar[rr,"\partial_{n+1}^C"]\ar[dd] && C_n\ar[rr,"\partial_n^C"]\ar[dd,"\varphi_n"',"\psi_n"]\ar[ddll,"T_n"'] && C_{n-1}\ar[ddll,"T_{n-1}"']\ar[r]\ar[dd] & \cdots\\\\ D: & \cdots\ar[r] & D_{n+1}\ar[rr,"\partial_{n+1}^D"] && D_n\ar[rr,"\partial_n^D",near end] && D_{n-1}\ar[r] & \cdots % \ar[from=1-5,to=1-7,color=blue,dash,start anchor={[xshift=-1em,yshift=3ex]center},end anchor={[xshift=3.8em,yshift=3ex]center}] \ar[from=3-3,to=3-5,color=blue,dash,start anchor={[xshift=-4em,yshift=-2ex]center},end anchor={[xshift=1em,yshift=-2ex]center}] \ar[from=3-3,to=1-5,color=blue,dash,start anchor={[xshift=-4em,yshift=-2ex]center},end anchor={[xshift=-1em,yshift=3ex]center}] \ar[from=1-7,to=3-5,color=blue,dash,start anchor={[xshift=3.8em,yshift=3ex]center},end anchor={[xshift=1em,yshift=-2ex]center}] \end{tikzcd}$

The problem is that tikz-cd doesn't allow one to use usual tikz commands inside the diagram, so I've just modeled the parallelogram by four edges (which are drawn as arrows without tips). The result is: