categories: Re: Query about Ab[C]

[Michael Barr <barr@barrs.org>]

I suspect that it is too much to hope for a characterization.  But it is
sufficient that either C or C^op be exact.  For C to be exact, it is
required that it have finite limits, coequalizers of equivalence
relations, that regular epis be stable under pullback and that every
equivalence relation is the kernel pair of its coequalizer.  

On Wed, 13 Dec 2000, Bill Rowan wrote:

> 
> Hi all,
> 
> Ab[C] is just my notation for the category of abelian group objects in
> the category C.  I was wondering if there is a simple characterization of
> those categories C for which Ab[C] is abelian.
> 
> Bill Rowan
>