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Type: Article
Characterization of Groupoids in Terms of Their Category of -Sets
Abstract:
A C-set is a functor from a category C to the category of finite sets, and C-set denotes the category of such functors with natural transformations as morphisms. In this work, we prove that C is a groupoid if and only if C-set has finitely many indecomposable objects, which is the categorical analog of transitive G-sets in classical group actions.
A C-set is a functor from a category C to the category of finite sets, and C-set denotes the category of such functors with natural transformations as morphisms. In this work, we prove that C is a groupoid if and only if C-set has finitely many indecomposable objects, which is the categorical analog of transitive G-sets in classical group actions.
Keywords: Groupoid||C-set||Indecomposable object||Burnside ring
Journal: Applied Categorical Structures
ISSN: 1572-9095
Year: 2026
Volume: 34
Pages: 21
Revision: 1
Notas: Scimago: Q1 Springer (Países bajos), EISSN: 1572-9095.
J. Miguel Calderón contó con el apoyo de SECIHTI con una beca postdoctoral de EPM. Alberto G. Raggi-Cárdenas e Itzel Rosas fueron parcialmente apoyados por la Beca de investigación UNAM-PAPIIT IN100226. Itzel Rosas también contó con el apoyo parcial de la Beca SECIHTI 4022250. Ramón H. Ruiz-Medina contó con el apoyo de la beca postdoctoral SECIHTI I1200/111/2024.
Created: 2026-04-21 12:48:46
Modified: 2026-04-21 12:50:31
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