Some remarks on connectors and groupoids in Goursat categories

We prove that connectors are stable under quotients in any (regular) Goursat category. As a consequence, the category $\mathsf{C}\mathsf{o}\mathsf{n}\mathsf{n}(\mathbb{C})$ 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.