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

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 $C^{\ast }$-algebras over a fixed Hausdorff étale groupoid.

19 pages