On Sun, Jun 7, 2009 at 1:37 AM, Andrew Salch<asalch@math.jhu.edu> wrote:
it is well-known (and proven e.g. in Hollander's PhD thesis) that categories fibered in groupoids over a small category C are equivalent to lax presheaves of groupoids on C. [...] I suspect there is some vast generalization of this, e.g. with the word "groupoids" replaced by "quasicategories" or something of that nature, which somebody has already proven, and in that case I would prefer to cite the more general result. Does anyone know if something like this is already in the literature?
Yes, see section 3.3.2 of Jacob Lurie's "Higher Topos Theory" for the statement for "quasicategory valued presheaves". [For admin and other information see: http://www.mta.ca/~cat-dist/ ]