In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.

Intrinsic Schreier Split Extensions / A. Montoli, D. Rodelo, T. Van der Linden. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 28:3(2020 Jun 01), pp. 517-538.

Intrinsic Schreier Split Extensions

A. Montoli;
2020

Abstract

In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.
Fibration of points; Jointly extremal-epimorphic pair; Jónsson–Tarski variety; Monoid; Protomodular category; Regular category; Unital category
Settore MAT/02 - Algebra
Settore MAT/01 - Logica Matematica
1-giu-2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/757229
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