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.
http://www.tac.mta.ca/tac/volumes/26/29/26-29.dvi
http://www.tac.mta.ca/tac/volumes/26/29/26-29.ps
http://www.tac.mta.ca/tac/volumes/26/29/26-29.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/29/26-29.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/29/26-29.ps
Revised 2014-12-12. Original version at
http://www.tac.mta.ca/tac/volumes/26/29/26-29a.pdf