Re: Fibrations in a 2-category

On Fri, Jan 14, 2011 at 12:02 AM, Michael Shulman <mshulman@ucsd.edu> wrote:

One way to deal with the difficulty you mention is by using "anafunctors," which were introduced by Makkai precisely in order to avoid the use of AC in category theory.

[...] Interesting. But before I ask for references on ``anafunctors'' I would like to know the following - is it false that for any (say) topos T there exists a category C whose 2-category of internal categories, functors, and natural transformations is (weakly) equivalent to the bicategory Cat_ana(T)? Best, MRP [For admin and other information see: http://www.mta.ca/~cat-dist/ ]