Abstract
We recall the notions of regular and exact categories. Then we show how the main results of protomodular categories concerning the split epimorphisms can be naturally extended to the regular epimorphisms when, moreover, the categories in question are regular or exact. Finally we prove that the pointed regular protomodular categories are characterized by the validity of the short five lemma.
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Bourn, D. (2017). Regular and homological categories. In: From Groups to Categorial Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-57219-2_5
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DOI: https://doi.org/10.1007/978-3-319-57219-2_5
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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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