In the course of certain studies on commutative rings, we needed the following result (to be sure, for ideals, not congruences): Let \Csc be a regular category and $f:A\to B$ an epimorphism in \Csc. Suppose $E_1$ and $E_2$ are congruences on $B$ with $D_1$ and $D_2$ their inverse images under $f\x f$. If the induced $A/D_1\to B/E_1$ is an isomorphism and $D_1\inc D_2$, then $E_1\inc E_2$ Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]