On certain 2-categories admitting localisation by bicategories of fractions

Pronk's theorem on bicategories of fractions is applied, in almost all cases in the literature, to 2-categories of geometrically presentable stacks on a 1-site. We give an proof that subsumes all previous such results and which is purely 2-categorical in nature, ignoring the nature of the objects involved. The proof holds for 2-categories that are not (2,1)-categories, and we give conditions for local essential smallness.David Michael Robert

The elementary construction of formal anafunctors

This article gives an elementary and formal 2-categorical construction of a bicategory of right fractions analogous to anafunctors, starting from a 2-category equipped with a family of covering maps that are fully faithful and co-fully faithful.Comment: v1: 20 pages, many diagrams. v2: updated after referee comments, 32 pages. v3: one minor terminology change, one proof streamlined after additional feedback, 32 page