Abstract
We quickly recall the main concepts of Category Theory with a strong emphasis on the universal property of pullbacks. A whole section is devoted to the art of recognizing them. We define monomorphisms, epimorphisms and split epimorphisms, the last notion being the pillar of our classification process of algebraic structures, via the fibration of points (see the classification table, page 103). Then we investigate the notion of internal equivalence relation and the subtle hierarchy related to the notion of epimorphism. Finally we describe the process of dualization of any categorical notion.
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Bourn, D. (2017). Basic concepts in category theory. In: From Groups to Categorial Algebra. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-57219-2_1
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DOI: https://doi.org/10.1007/978-3-319-57219-2_1
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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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