Some time ago I wrote notes constructing in a purely 2-categorical language a bicategory of anafunctors, starting from a 2-category $K$ equipped with a notion of cover, which in the original setting that Makkai studied, reduces to a trivial isofibration of categories. I always wanted to do something more with the construction, and I still do, but I thought it worthwhile to get the notes into a shape suitable for public consumption (at one point I had changed notational convention, and I found this week that the transition was half-way through a diagram!). So here they are:

The elementary construction of formal anafunctors,arXiv:1808.04552, doi:10.25909/5b6cfd1a73e55

Abstract:These notes give an elementary and formal 2-categorical construction of the bicategory of anafunctors, starting from a 2-category equipped with a family of covering maps that are fully faithful.

As always, comments welcome.