# Some remarks on connectors and groupoids in Goursat categories

## TL;DR

This paper demonstrates that connectors are stable under quotients in Goursat categories, leading to a new characterization of Goursat categories via properties of internal groupoids, thus advancing the understanding of categorical structures.

## Contribution

It proves the stability of connectors under quotients in Goursat categories and characterizes Goursat categories through internal groupoid properties.

## Key findings

- Connectors are stable under quotients in Goursat categories.
- The category of connectors inherits Goursat properties.
- Goursat categories can be characterized by internal groupoid properties.

## 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.