Faithfully flat descent for magmas
| Autor: | J. M. Fernández Vilaboa, M.P. López López, J. N. Alonso Álvarez, R. González Rodríguez |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Unital 010102 general mathematics Monoidal category 01 natural sciences Magma (computer algebra system) Morphism Mathematics::Category Theory Monoid (category theory) 0103 physical sciences 010307 mathematical physics 0101 mathematics computer Descent (mathematics) computer.programming_language Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 224:586-609 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2019.06.002 |
| Popis: | In this paper we develop a descent theory for morphisms α between a monoid B and a unital magma A in a monoidal category with equalizers and coequalizers. We introduce the category of strong descent data for α and we prove that under faithfully flat conditions this category is equivalent to the one of right B-modules. As an application we prove that the category of strong Hopf modules, introduced by us for Hopf quasigroups and weak Hopf quasigroups, is equivalent to a suitable category of strong descent data. |
| Databáze: | OpenAIRE |
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