Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$

Francis Borceux; Federico Campanini; Marino Gran; Walter Tholen

doi:10.1016/j.aim.2023.109110

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arXiv · 2207.08487

Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$

Francis Borceux·Federico Campanini·Marino Gran·Walter Tholen

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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.

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Francis Borceux, Federico Campanini, Marino Gran, Walter Tholen. 2022-07-18. Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$. https://doi.org/10.1016/j.aim.2023.109110

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