Geodesic
Maschke type theorems for Hopf monoids
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 9-47

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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.

Publié le :
Classification : 18M50, 18N10, 18C15, 16T05
Keywords: duoidal category, Hopf monoid, monoidal bicategory, naturally Frobenius map monoidale, Masche theorem, separability, integral 
@article{TAC_2021_36_a0,
     author = {Gabriella B\"ohm},
     title = {Maschke type theorems for {Hopf} monoids},
     journal = {Theory and applications of categories},
     pages = {9--47},
     publisher = {mathdoc},
     volume = {36},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a0/}
}
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Gabriella Böhm. Maschke type theorems for Hopf monoids. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 9-47. http://geodesic.mathdoc.fr/item/TAC_2021_36_a0/