Fundamental groupoids for simplicial objects in Mal'tsev categories

0535229 - MÚ 2022 RIV NL eng J - Journal Article
Duvieusart, Arnaud
Fundamental groupoids for simplicial objects in Mal'tsev categories.
Journal of Pure and Applied Algebra. Roč. 225, č. 6 (2021), č. článku 106620. ISSN 0022-4049. E-ISSN 1873-1376
Institutional support: RVO:67985840
Keywords : central extensions * Galois theory * internal groupoids * Mal'tsev categories
OECD category: Pure mathematics
Impact factor: 0.834, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.jpaa.2020.106620

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).
Permanent Link: http://hdl.handle.net/11104/0313307