I'll try again... On Mon, Oct 24, 2011 at 11:23 AM, Dmitry Roytenberg <starrgazerr@gmail.com> wrote:
Dear category theorists,
It is well known that any functor that preserves finite limits preserves monomorphisms, and that for an additive right-exact functor between abelian categories, the converse is also true. Is it known how far this extends to the non-additive setting? In other words, what exactness properties of two categories and a functor between them would suffice to conclude that the functor preserves finite limits if and only if it preserves monos? For instance, is it enough to assume that the categories be Barr-exact and that the functor preserve all colimits, finite products and monos to conclude that it also preserves equalizers?
Any references would be extremely helpful.
Thanks, Dmitry
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