On groupoid-graded C*-algebras and equivalent subcategories linked via monads and comonads

TL;DR

This paper introduces a categorical approach using monads and comonads to establish equivalences of subcategories, demonstrated through topological gradings of C*-algebras over Hausdorff étale groupoids.

Contribution

It develops a novel categorical framework to analyze subcategory equivalences in the context of C*-algebras and groupoid gradings.

Findings

New categorical method for subcategory equivalence

Application to topological gradings of C*-algebras

Enhanced understanding of groupoid-graded C*-algebras

Abstract

We present a new method, involving monads and comonads from category theory, to help establish a certain type of equivalence of subcategories. As a case study we consider the category of topological gradings of $C^*$-algebras over a fixed Hausdorff \'etale groupoid.