Dear Mike,
Does it not work to say that every internal category admits a weak equivalence functor to an internal category which is a stack?
Sure. This is so by Corollary 2.11 in Bunge-Pare. No problem with internal categories or internal weak equivalence functors of course. But how does one internalize the notion of a stack? It comes down to parametrizing all epimorphisms in the topos itself. All the best,Marta ----------------------------------------
Date: Tue, 12 Jul 2011 11:45:41 -0700 Subject: Re: categories: RE: stacks (was: size_question_encore) From: mshulman@ucsd.edu To: marta.bunge@mcgill.ca CC: david.roberts@adelaide.edu.au; joyal.andre@uqam.ca; categories@mta.ca
On Tue, Jul 12, 2011 at 7:56 AM, Marta Bunge <martabunge@hotmail.com> wrote:
As for stacks being the primary motivation Makkai had for anafunctors, that is not the impression I got from people attending his course,
Okay, thanks for the correction.
I forgot to mention that an elementary formulation of ASC ("axiom of stack completions") is till missing.
Does it not work to say that every internal category admits a weak equivalence functor to an internal category which is a stack?
Mike
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