RE: stacks (was: size_question_encore)

[Marta Bunge <martabunge@hotmail.com>]

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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