A 2-colimit characterization of internal categories of torsors
By using the associated fibration, the author defines and proves the existence of the 2-colimit of a 2-pseudofunctor from a 2-category to CAT. For an internal category B in an exact category he defines Tors(1,B) to be torsors over B (presheaves on B whch become representable upon pullback over some regular epimorphism \(C\to 1)\), and \(Tor_ C(1,B)\) to be torsors representable for a particular \(C\to 1\). The \(Tor_ C(1,B)\) then define a 2-pseudofunctor from the 2-category of codiscrete groupoids to CAT whose 2-colimit is Tors(1,B). This generalizes the familiar Čech construction for principal fibre bundles.
scientific article; zbMATH DE number 4212291