Shifting curved line downwards in xymatrix

Question

In the following MEW I have two problems

1. Only due to the MWE: stackexchange is having some problem highlighting my code (due to the back upper coma)
2. The real problem: I would like that the snake go through in the middle, between V,WZ and rho1,rho2,rho3.

    \documentclass{article}
    \usepackage[all]{xy}
    \usepackage{amsmath}
    \begin{document}
\xymatrix@C=1pc{
&&\operatorname{ker}(\rho_1) \ar[rr]\ar[d]^-{\iota_1}
  &&\operatorname{ker}(\rho_2) \ar[rr]\ar[d]^-{\iota_2}
  &&\operatorname{ker}(\rho_3) \ar[d]^-{\iota_3}
    \ar`r[d]`[ll]`[llllld]`[dddllll][dddllll]  \\
&&V \ar[rr]^{\phi}\ar[d]^{\rho_1}
  &&W \ar[rr]^{\psi}\ar[d]^{\rho_2}
  &&Z \ar[rr]\ar[d]^{\rho_3}&&0\\
0\ar[rr] &&V' \ar[rr]^{\phi'}\ar[d]^-{\pi_1}
    &&W' \ar[rr]^{\psi'}\ar[d]^-{\pi_2}
    &&Z'\ar[d]^-{\pi_3} &&\\
&&\operatorname{coker}(\rho_1)\ar[rr]
  &&\operatorname{coker}(\rho_2)\ar[rr]
  &&\operatorname{coker}(\rho_3)&&
}

\end{document}

Answer 1

From the old question How do you draw the "snake" arrow for the connecting homomorphism in the snake lemma? you can adapt your code. Here I have put part of your letters.

\documentclass[12pt]{article}
\usepackage[all]{xy}
\usepackage{amsmath}
\DeclareMathOperator{\coker}{coker}
\newcommand*\pp{{\rlap{\('\)}}}
\begin{document}
%
\[
  \xymatrix@!{
              && {\ker(\rho_1)} \ar[r]   & {\ker(\rho_2)} \ar[r]   & {\ker(\rho_3)}
                    \ar`r[d]`[l]`^d[lll]|!{[];[d]}\hole|!{[l];[dl]}\hole|!{[ll];[dll]}\hole
                    `[dddll]|!{[ddllll];[ddll]}\hole [dddll]
                                                                       &   \\
              && A  \ar[r]^{f}      & B  \ar[r]^{g}      & C \ar[r]    & 0 \\
    0 \ar[rr] && A\pp \ar[r]^{f'}   & B\pp \ar[r]^{g'}   & C\pp        &   \\
              && {\coker(a)} \ar[r] & {\coker(b)} \ar[r] & {\coker(c)} &   \\
    % vertical arrows
    \ar"1,3";"2,3"^{\iota_1}   \ar"1,4";"2,4"   \ar"1,5";"2,5"
    \ar"2,3";"3,3"^a \ar"2,4";"3,4"^b \ar"2,5";"3,5"^c
    \ar"3,3";"4,3"   \ar"3,4";"4,4"   \ar"3,5";"4,5"
  }
\]
\end{document}

Answer 2

A pstricks solution:

\documentclass{article}
\usepackage{mathtools}
\DeclareMathOperator{\coker}{coker}
\usepackage{pst-node, multido}
\begin{document}
$ \psset{arrows=->, arrowinset=0.15, linewidth=0.6pt, linejoin=1, nodesep=2pt, rowsep=0.75cm, colsep=0.8cm, shortput =tablr, labelsep=1.5pt}
\everypsbox{\scriptstyle}
\begin{psmatrix}[mnode = R]
  %%% nodes
    & \ker(\rho_1) & \ker(\rho_2) &\ker(\rho_3)\
    & V & W & Z & 0 \pnode[0,-0.3cm]{I}\
    0 & V' & W' & Z' \
    & \coker(\rho_1) & \coker(\rho_2) &\coker(\rho_3)
   %%% snake arrow
    {\psset{linearc=0.4}%
     \ncbar[arrows=-, armA=1.2cm, nodesepB=0pt]{1,4}{I}
     \ncbar[angle=180, armB=1.2cm, nodesepA=0pt]{I}{4,2}}
    %%% horizontal arrows%
 \foreach \s/\t in {2/3,3/4}{\ncline{1,\s}{1,\t}\ncline{4,\s}{4,\t}}
 \ncline{2,2}{2,3}^{\phi } \ncline{2,3}{2,4}^{\psi } \ncline{2,4}{2,5}
 \ncline{3,1}{3,2}\ncline{3,2}{3,3}^{\phi'} \ncline{3,3}{3,4}^{\psi'}
  %%% vertical arrows
    \psset{border=1.5pt}
    \foreach \i/\c in {1/2,2/3,3/4}{\ncline{1,\c}{2,\c}>{\iota_\i} \ncline{2,\c}{3,\c}>{\rho_\i} %
    \ncline{3,\c}{4,\c}>{\pi_\i}}
\end{psmatrix}$
\end{document}