Characterization of groupoid categories in terms of its category of C-sets

2025/08/13 by Calderón, J. Miguel, Raggi-Cárdenas, Alberto Gerardo, Rosas, Itzel +1
#18A25 #18B40 #19A22 #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2508.10162

Abstract

A C-set is a functor from the category C to the category of finite sets and functions. The category of C-sets, C - \operatorname*set, is defined as the category whose objects are C-sets, and whose morphisms are natural transformations between them. In this document we provide some concise characterizations of groupoids in terms of their category of C-sets.

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