Products of epimorphisms

[David Yetter <dyetter@ksu.edu>]

Dear fellow category theorists,

I'm interested in finding out at what level of generality a result that plainly holds in Sets (and Sets^op) is true:

Given two epimorphisms f:A-->>B and g:C-->D, the square formed by f x 1_C, 1_A x g, f x 1_D and 
1_B x D is a pushout.

I'd like it to be true (at least) in toposes and I think I have an element-wise proof (but don't remember the details of the semantics given by, for instance, Osius, well enough to be sure I've really proven the result in all  toposes -- it's been years since I thought seriously about that sort of thing).

And, is there anywhere in the literature that this occurs?  It feels like the sort of thing that would have been known long ago.

Best Thoughts,
David Yetter
Professor of Mathematics
Kansas State University




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