An introduction to regular categories. (English) Zbl 1480.18007
Clementino, Maria Manuel (ed.) et al., New perspectives in algebra, topology and categories. Summer school, Louvain-la-Neuve, Belgium, September 12–15, 2018 and September 11–14, 2019. Cham: Springer. Coimbra Math. Texts 1, 113-145 (2021).
Summary: This paper provides a short introduction to the notion of regular category and its use in categorical algebra. We first prove some of its basic properties, and consider some fundamental algebraic examples. We then analyse the algebraic properties of the categories satisfying the additional Mal’tsev axiom, and then the weaker Goursat axiom. These latter contexts can be seen as the categorical counterparts of the properties of 2-permutability and of 3-permutability of congruences in universal algebra. Mal’tsev and Goursat categories have been intensively studied in the last years: we present here some of their basic properties, which are useful to read more advanced texts in categorical algebra.
For the entire collection see [Zbl 1475.18001].
For the entire collection see [Zbl 1475.18001].
MSC:
| 18E08 | Regular categories, Barr-exact categories |
| 18E13 | Protomodular categories, semi-abelian categories, Mal’tsev categories |
| 18C05 | Equational categories |
| 08B05 | Equational logic, Mal’tsev conditions |
Keywords:
regular category; Mal’tsev category; Goursat category; variety of algebras; Mal’tsev conditionsCitations:
Zbl 1475.18001References:
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