On the Naturalness of Mal’tsev Categories

Bourn, Dominique; Gran, Marino; Jacqmin, Pierre-Alain

doi:10.1007/978-3-030-66545-6_3

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2021

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Cited by 2 publications

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“…Any protomodular category is a Mal'tsev one. In a regular (and a fortiori exact) Mal'tsev category, any base-change functor f * along a regular epimorphism f is fully faithful and fibrant on monomorphisms by Theorem 52 in [9]. It remains to show that, in the exact context, this is the case for any base-change m * along a monomorphims m as well.…”

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confidence: 92%

Normalizers in the non-pointed context: a weak case of extremal decomposition

Bourn¹

2021

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The aim of this work is to point out a strong structural phenomenon hidden behind the existence of normalizers through the investigation of this property in the non-pointed context: given any category E, a certain property of the fibration of points ¶ E : P t(E) → E guarentees the existence of normalizers. This property becomes a characterization of this existence when E is quasi-pointed and protomodular. This property is also showed to be equivalent to a property of the category GrdE of internal groupoids in E which is a kind of opposite, for the monomorphic internal functors, of the comprehensive factorization.

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confidence: 92%