Fundamental groupoids for simplicial objects in Mal'tsev categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00535229" target="_blank" >RIV/67985840:_____/21:00535229 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jpaa.2020.106620" target="_blank" >https://doi.org/10.1016/j.jpaa.2020.106620</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2020.106620" target="_blank" >10.1016/j.jpaa.2020.106620</a>

Result language
angličtina
Original language name
Fundamental groupoids for simplicial objects in Mal'tsev categories
Original language description
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).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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