×

Some remarks on connectors and groupoids in Goursat categories. (English) Zbl 1453.18004

Summary: We prove that connectors are stable under quotients in any (regular) Goursat category. As a consequence, the category \(\mathsf{Conn}(\mathbf{C})\) of connectors in \(\mathbf{C}\) is a Goursat category whenever \(\mathbf C\) is. This implies that Goursat categories can be characterised in terms of a simple property of internal groupoids.

MSC:

18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
08B05 Equational logic, Mal’tsev conditions
18B10 Categories of spans/cospans, relations, or partial maps
PDF BibTeX XML Cite
Full Text: DOI arXiv