Internal categories, anafunctors and localisations

David Michael Roberts

In this article we review the theory of anafunctors introduced by Makkai and Bartels, and show that given a subcanonical site $S$, one can form a bicategorical localisation of various 2-categories of internal categories or groupoids at weak equivalences using anafunctors as 1-arrows. This unifies a number of proofs throughout the literature, using the fewest assumptions possible on $S$.

Keywords: internal categories, anafunctors, localization, bicategory of fractions

2010 MSC: Primary 18D99;Secondary 18F10, 18D05, 22A22

Theory and Applications of Categories, Vol. 26, 2012, No. 29, pp 788-829.

Published 2012-12-21.

Revised 2014-12-12. Original version at

TAC Home