Authors: Marino Gran ; Diana Rodelo ; Idriss Tchoffo Nguefeu

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

• 08B05 - Equational logic, Mal'tsev conditions
• 18B10 - Categories of spans/cospans, relations, or partial maps
• 18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories)