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An introduction to regular categories

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Gran, Marino [UCL]

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 ana-lyse 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.

Document type Contribution à ouvrage collectif (Book Chapter)
Access type Accès libre
Publication date 2021
Language Anglais
Host document M.M. Clementino, A. Facchini and M. Gran ; "New Perspectives in Algebra, Topology and Categories"- 113-145 (ISBN : 978-3-030-84319-9)
Collection Coimbra Mathematical Texts - 1 (ISSN : 2813-0057)
Edition statement Springer
Peer reviewed yes
Publisher Springer (Coimbra)
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Regular category ; Relations ; Mal'tsev category ; Goursat category
Links
Bibliographic reference Gran, Marino. An introduction to regular categories. In: M.M. Clementino, A. Facchini and M. Gran, New Perspectives in Algebra, Topology and Categories, Springer  : Coimbra 2021, p.113-145
Permanent URL http://hdl.handle.net/2078.1/231875