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arXiv · 2110.14280

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

Dominique Bourn
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Abstract

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: Pt(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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Dominique Bourn. 2021-10-27. Normalizers in the non-pointed context: a weak case of extremal decomposition. https://arxiv.org/abs/2110.14280

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