# Michael Shulman Beck-Chevalley condition > history

For any subobject $U$ of $B$, $g:C\to A$, $f:B\to A$, $q:C{\times}B\to A$ and $p:C{\times}B\to B$,

$g^{-1}\exists_{f}U=\exists_{q}p^{-1}U$

See Mac Lane and Moerdijk, section IV.9 (page 205).

Last revised on December 20, 2009 at 06:51:51. See the history of this page for a list of all contributions to it.