Abstract
We noticed that in the category Gp of groups any reflexive relation is necessarily an equivalence relation. A category fulfilling this property is called a Mal’tsev category. In chapter 4, we showed that any protomodular category is a Mal’tsev one. In this chapter, we investigate the notion of Mal’tsev categories for its own. We introduce the notion of centralization of equivalence relations and of affine object. Finally we characterize the Mal’tsev categories by a property of the fibration of points.
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Bourn, D. (2017). Mal’tsev and naturally Mal’tsev categories. In: From Groups to Categorial Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-57219-2_7
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DOI: https://doi.org/10.1007/978-3-319-57219-2_7
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-57218-5
Online ISBN: 978-3-319-57219-2
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