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Normal sections and direct product decompositions

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Bourn, D Gran, Marino [UCL]

In any finitely complete category, there is an internal notion of normal monomorphism. We give elementary conditions guaranteeing that a normal section s : Y --> X of an arrow f : X --> Y produces a direct product decomposition of the form X similar or equal to Y x W. We then show how these conditions gradually vanish in various algebraic contexts, such as Maltsev, protomodular and additive categories.

Document type Article de périodique (Journal article)
Publication date 2004
Language Anglais
Journal information "Communications in Algebra" - Vol. 32, no. 10, p. 3825-3842 (2004)
Peer reviewed yes
issn 0092-7872
Publication status Publié
Affiliation UCL - Autre
Links
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Bibliographic reference Bourn, D ; Gran, Marino. Normal sections and direct product decompositions. In: Communications in Algebra, Vol. 32, no. 10, p. 3825-3842 (2004)
Permanent URL http://hdl.handle.net/2078/84353