An introduction to regular categories
Abstract
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 -permutability and of -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.
Cite
@article{arxiv.2004.08964,
title = {An introduction to regular categories},
author = {Marino Gran},
journal= {arXiv preprint arXiv:2004.08964},
year = {2022}
}
Comments
27 pages, lecture notes of a mini-course given at the Summer School in Algebra and Topology held at the Institut de Recherche en Math\'ematique et Physique of the Universit\'e catholique de Louvain, 11th-14th September 2019