Abstract
Here, we introduce the main concept of this book, namely the notion of protomodular category. We show how any pointed protomodular category retains the five main striking features of the category Gp of groups:
(a) an injective homomorphism is characterized by the triviality of its kernel
(b) a surjective homomorphism is necessarily the cokernel of its kernel
(c) there is a specific class of subobjects, namely the normal subobjects
(d) being commutative is a property
(e) any internal reflexive relation is an equivalence relation.
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Bourn, D. (2017). Unital and protomodular categories. In: From Groups to Categorial Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-57219-2_4
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DOI: https://doi.org/10.1007/978-3-319-57219-2_4
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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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