## 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
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