diagramsxy-pic
I need to use the xy maths package (because I need to make it into a PNG file for WordPress and mathurl.com accepts the xy template) to make a commutative diagram in which there are diagonal 4 shorter arrows inside the diagram, directed inward. The best I can do is
\usepackage[all]{xy}
\xymatrix{Y' \ar[r]^{g'}
\ar[d]_{f'} & X' \ar[d]^{f} \\
Y \ar[r]_{g} & X
\\
%
\ar@{=>}"1,2"*++++\frm{};"2,1"*++\frm{}}
So I can only get one arrow, which needs to be higher up to the right.
In Xy-pic:
\documentclass{article}
\usepackage[all,2cell]{xy}
\UseAllTwocells
\begin{document}
\xymatrixcolsep{3cm}
\xymatrix{
A \ruppertwocell^f{\alpha}
\rlowertwocell_h{\beta}
\ar[r]|{g}
&B\\
}
\end{document}
In TikZ:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning,arrows}
\begin{document}
\begin{tikzpicture}
\node (a) {$A$};
\node[right=4cm of a] (b) {$B$};
\draw[->]
(a) edge node[fill=white] (g) {$g$} (b)
(a) edge[bend left] node (f) [above]{$f$} (b)
(a) edge[bend right] node (h) [below]{$h$} (b);
\draw[shorten <=2pt,shorten >=2pt,-implies]
(f) edge[double] (g)
(g) edge[double] (h);
\end{tikzpicture}
\end{document}
Here's a possible solution using the color option for the xy package and the xcolor package:
\documentclass{article}
\usepackage{xcolor}
\usepackage[all,color]{xy}
\begin{document}
\xymatrix{
& & H(Z) \ar@/^2.0pc/@[red][rr]^{F(f^{op} \circ g^{op})} \ar[r]^{H^{*}(g^{op})}
& H(Y) \ar@{=}[dl] \ar[r]^{H^{*}(f^{op})}
& H(X) \ar@{=}[dl] \ar@/^2.0pc/@{=>}@[red][ddll] \\
& H(Z) \ar@{=}[ur]
& H(Y) \ar[u]_{G(g^{op})}
& H(X) \ar@{=}[dl] \ar[u]_{G(f^{op})} \\
H(Z) \ar[r]_{H^{*}(g^{op})} \ar@{=}[ur]
& H(Y) \ar@{=}[ur] \ar[r]_{H^{*}(f^{op})} \ar[u]_{G(g^{op})}
& H(X) \ar[u]_{G(f^{op})}
\ar@/^2.0pc/@[red][uu]^{G(f^{op} \circ g^{op})}
}
\end{document}
The above code will produce the following result (I only focused my answer on the problems mentioned in the question; the layout of the diagram has to be improved to avoid overlapping elements):
Changing the column spacing, overlapping element are prevented:
\documentclass{article}
\usepackage{xcolor}
\usepackage[all,color]{xy}
\begin{document}
\xymatrix@C=2cm{
& & H(Z) \ar@/^2.0pc/@[red][rr]^{F(f^{op} \circ g^{op})} \ar[r]^{H^{*}(g^{op})}
& H(Y) \ar@{=}[dl] \ar[r]^{H^{*}(f^{op})}
& H(X) \ar@{=}[dl] \ar@/^2.0pc/@{=>}@[red][ddll] \\
& H(Z) \ar@{=}[ur]
& H(Y) \ar[u]_{G(g^{op})}
& H(X) \ar@{=}[dl] \ar[u]_{G(f^{op})} \\
H(Z) \ar[r]_{H^{*}(g^{op})} \ar@{=}[ur]
& H(Y) \ar@{=}[ur] \ar[r]_{H^{*}(f^{op})} \ar[u]_{G(g^{op})}
& H(X) \ar[u]_{G(f^{op})}
\ar@/^2.0pc/@[red][uu]^{G(f^{op} \circ g^{op})}
}
\end{document}
As a side note, a package that could be of interest for you is tikz-cd.
Best Answer
I'd use additional rows and columns: