The groupoid structure of groupoid morphisms

TL;DR

This paper constructs and compares two types of groupoids derived from groupoid morphisms, establishing their equivalence, and explores the automorphism groupoid of a given groupoid from both categorical and geometric perspectives.

Contribution

It introduces two new constructions of groupoids from morphisms and proves their equivalence, providing insights into the structure of automorphisms of groupoids.

Findings

Two groupoids of morphisms are equivalent.

Constructed from categorical and geometric viewpoints.

Analyzed the automorphism groupoid of a groupoid.

Abstract

In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are equivalent. Then we study the automorphism groupoid of a groupoid.