Short diagonal arrows inside commutative diagram

Question

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.

Answer 1

I'd use additional rows and columns:

\xymatrix@R.8pc@C.8pc{
Y' \ar[rr]^{g'} \ar[dd]_{f'} && X' \ar[dd]^{f} \\
 & \mbox{\phantom{$x$}} \ar@{<=}[ul] \ar@{<=}[ur] \ar@{<=}[dl] \ar@{<=}[dr]   & \\
Y \ar[rr]_{g} && X
}