Monads and etale groupoid Fell bundles

Several constructions in operator algebras have given rise to closely linked (``associated'') subcategories. These involve universal properties, which are sometimes not easy to verify. We introduce a new method - involving monads and comonads - to make this easier. And we apply it to a new example: Fell bundles over etale groupoids. Work in progress. Joint work with Erik Bedos and S. Kaliszewski.