On morphisms of topological quivers

TL;DR

This paper introduces regular morphisms of topological quivers, establishing a subcategory and demonstrating that the associated C*-algebra construction is a contravariant functor, enriching the categorical framework of topological quivers.

Contribution

It defines regular morphisms for topological quivers and shows these induce a functor to C*-algebras, expanding the categorical understanding of quiver C*-algebras.

Findings

Regular morphisms form a subcategory of topological quivers.

The C*-algebra construction is a contravariant functor.

Establishes categorical relationships between quivers and C*-algebras.

Abstract

We introduce regular morphisms of topological quivers and show that they give rise to a subcategory of the category of topological quivers and quiver morphisms. Our regularity conditions render the topological quiver C*-algebra construction a contravariant functor from the category of topological quivers and regular morphisms into the category of C*-algebras and $*$-homomorphisms.