Mathematics > Category Theory
[Submitted on 18 Jul 2022 (v1), last revised 10 May 2023 (this version, v2)]
Title:Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$
View PDFAbstract: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.
Submission history
From: Marino Gran [view email][v1] Mon, 18 Jul 2022 10:12:49 UTC (45 KB)
[v2] Wed, 10 May 2023 15:45:47 UTC (45 KB)
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