A 2-colimit characterization of internal categories of torsors
type: Item
instance of: scholarly article
title: A 2-colimit characterization of internal categories of torsors
zbMATH Open document ID: 0733.18008
DOI: 10.1016/0022-4049(91)90041-Y
author: K. T. S. Mohapeloa
published in: Journal of Pure and Applied Algebra
publication date: 1991-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 18F15
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 4212291
zbMATH Keywords: 2-colimit
zbMATH Keywords: 2-pseudofunctor
zbMATH Keywords: 2-category
zbMATH Keywords: internal category
zbMATH Keywords: exact category
zbMATH Keywords: torsors
zbMATH Keywords: presheaves
zbMATH Keywords: codiscrete groupoids
zbMATH Keywords: principal fibre bundles
reviewed by: Don H. Van Osdol
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4212291