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Normalizers in the non-pointed context
Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 32-62 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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 \P_E: 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 Grd E of internal groupoids in E which is almost opposite, for the monomorphic internal functors, of the comprehensive factorization.

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Classification : 18A05, 18B99, 18E13, 08C05, 08A30, 08A99
Keywords: equivalence relation, equivalence class, normal subobject, normalizers, Mal'tsev and protomodular categories, internal categories and groupoids, comprehensive factorization, non-pointed additive categories 
@article{TAC_2024_40_a1,
     author = {Dominique Bourn},
     title = {Normalizers in the non-pointed context},
     journal = {Theory and applications of categories},
     pages = {32--62},
     year = {2024},
     volume = {40},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_40_a1/}
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Dominique Bourn. Normalizers in the non-pointed context. Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 32-62. http://geodesic.mathdoc.fr/item/TAC_2024_40_a1/