Fundamental groupoids for simplicial objects in Mal'tsev categories

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Duvieusart, Arnaud^1,2 

[1] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2, B-1348 Louvain La Neuve, Belgium

[2] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567, Czech Republic

关键词: Mal'tsev categories;    Internal groupoids;    Simplicial objects;    Galois theory;    Central extensions;    Monotone-light factorization;   

DOI  :  10.1016/j.jpaa.2020.106620

来源: Elsevier

【 摘 要 】

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini). (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free