Distributors and the comprehensive factorization system for internal groupoids

TL;DR

This paper demonstrates that distributors between groupoids in a Barr-exact category form a bicategory of relations aligned with the comprehensive factorization system, providing a new perspective on internal groupoids.

Contribution

It establishes a connection between distributors and the comprehensive factorization system in the context of internal groupoids in Barr-exact categories.

Findings

Distributors form a bicategory of relations in this setting.

The bicategory aligns with the comprehensive factorization system.

Provides a new framework for understanding internal groupoids.

Abstract

In this note we prove that distributors between groupoids in a Barr-exact category E form the bicategory of relations relative to the comprehensive factorization system in Gpd(E). Revised version.