A Characterization of Groupoids in Terms of Their Category of $\mathcal {C}$-Sets

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2026年4月4日

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J. Miguel Calderón,
Alberto G. Raggi-Cárdenas,
Itzel Rosas,
Ramón H. Ruiz-Medina

摘要

A $\mathcal {C}-\text {set}$ $C - set$ is a functor from a category $\mathcal {C}$ $C$ to the category of finite sets, and $\mathcal {C}-\text {set}$ $C - set$ denotes the category of such functors with natural transformations as morphisms. In this work, we prove that $\mathcal {C}$ $C$ is a groupoid if and only if $\mathcal {C}-\text {set}$ $C - set$ has finitely many indecomposable objects, which is the categorical analog of transitive G-sets in classical group actions.

A Characterization of Groupoids in Terms of Their Category of \(\mathcal {C}\)-Sets

摘要