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
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