[Xy-pic] Descent of displaymode

[Michael Barr]

Is there any way of getting displaymode to descend into xy-pic?  Here is a 
sample file:

\documentclass{article}
\usepackage[arrow]{xy}
\begin{document}

 \[\xy
\POS(0,0)*+!!<0ex,.55ex>{\prod_{i\in I}L_i}\ar@{>}
(0,-20)*+!!<0ex,.55ex>{\prod_{j\in J}L_j}%
\endxy\]

\end{document}

The subscripts look silly.  Of course, I write \prod\limits_{i\in I}L_i, 
but that is a nuisance.  Is there any way of making that the default.  Of 
course, I don't want \limits built-in, only for macros that normally do it 
in displaymode.  It makes no difference, incidentally, if you use \[...\] 
or $$...$$.

Michael