Abstract
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.
Highlights
Anafunctors were introduced by Makkai [7] as new 1-arrows in the 2-category Cat to talk about category theory in the absence of the axiom of choice
V0 2 $ g2 G x( 3 where the last equality holds as u2v2 → v2 is ff, so we can lift ak to a1
Summary
Anafunctors were introduced by Makkai [7] as new 1-arrows in the 2-category Cat to talk about category theory in the absence of the axiom of choice. This article has had a long and tortuous history It started out as the second half of what was published as [12], in an attempt to give an elementary and completely self-contained proof ommitting no details of the results of [8] dealing with 2-categories of stacks as bicategorical localisations. In this the author was partially influenced by the late Vladimir Voevodsky’s insistence on details and constructions in what might otherwise seem merely bureaucratic proofs. Work in preparation using cospans to localise 2-categories of topological groupoids required the machinery of the present paper, in its dual incarnation, so it is hoped there is some merit in the elementary approach in it
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