Re: when does preservation of monos imply left exactness?

[Dmitry Roytenberg <starrgazerr@gmail.com>]

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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