Maschke type theorems for Hopf monoids

Gabriella Böhm

We study integrals of Hopf monoids in duoidal endohom categories of naturally Frobenius map monoidales in monoidal bicategories. We prove two Maschke type theorems, relating the separability of the underlying monoid and comonoid, respectively, to the existence of normalized integrals. It covers the examples provided by Hopf monoids in braided monoidal categories, weak Hopf algebras, Hopf algebroids over central base algebras, Hopf monads on autonomous monoidal categories and Hopf categories.

Keywords: duoidal category, Hopf monoid, monoidal bicategory, naturally Frobenius map monoidale, Masche theorem, separability, integral

2020 MSC: 18M50, 18N10,18C15, 16T05

Theory and Applications of Categories, Vol. 36, 2021, No. 1, pp 9-47.

Published 2021-03-01.

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