Some remarks on connectors and groupoids in Goursat categories

Abstract

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.

Keywords

• mathematics - category theory
• mathematics - rings and algebras
• 08c05, 08b05, 08a30, 08b10, 18c05, 18e10