Re: Re: when does preservation of monos imply left exactness?

[Dmitry Roytenberg <starrgazerr@gmail.com>]

Dear George,

Well, I find Barr's theorem useful insomuch as it highlights regular
monos as the relevant ones and thereby brings the situation into
sharper focus: proving the preservation of the equalizers of cokernel
pairs should be easier than arbitrary ones. Of course, characterizing
the regular monos and proving that they are preserved by cobase change
(I've finally remembered what A@- is called!) could be a difficult
matter, depending on the circumstances.

So, I thank everyone for the feedback. I will post here if I manage to
prove anything of interest.

Best,

Dmitry

On Sun, Oct 30, 2011 at 1:10 AM, George Janelidze <janelg@telkomsa.net> wrote:
> Dear Dmitry,
>
> Absolutely correct (although it does not change anything I said).
>
> Thank you for explaining "why". So your real question is about preservation
> of finite limits by functors of the form A+(-), in the case non-commutative
> algebras (of various kinds). Well, from this point of view the categories  of
> algebras are 'difficult', and I don't recall any reasonable result at the
> moment. Moreover, I am surprised that Barr's theorem helps here (which does
> not mean that the theorem itself is not good of course!), and I would be
> very interested to learn, what exactly could you deduce from it?
>
> Best regards,
>
> George
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]