Groupoids and skeletal categories form a pretorsion theory in Cat

Borceux, Francis;Campanini, Federico;Gran, Marino;Tholen, Walter Paul
(2023) Advances in mathematics — Vol. 426, p. 109110 (2023)

Files

PretorsionCAT14-07-22.pdf
  • Open Access
  • Adobe PDF
  • 267.97 KB
Download

Details

Authors
Abstract
We describe a pretorsion theory in the category Cat of small categories: the torsion objects are the groupoids, while the torsion-free objects are the skeletal categories, i.e., those categories in which every isomorphism is an automorphism. We infer these results from two unexpected properties of coequalizers in Cat that identify pairs of objects: they are faithful and reflect isomorphisms.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Borceux, F., Campanini, F., Gran, M., & Tholen, W. P. (2023). Groupoids and skeletal categories form a pretorsion theory in Cat. Advances in mathematics, 426, 109110. https://hdl.handle.net/2078.5/268883 (Original work published 2023)