Hopf monoidal comonads

Dimitri Chikhladze, Stephen Lack, and Ross Street

We generalize to the context internal to an autonomous monoidal bicategory the work of Bruguieres, Virelizier, and the second-named author on lifting closed structure on a monoidal category to the category of Eilenberg-Moore algebras for an opmonoidal monad. The result then applies to quantum categories and bialgebroids.

Keywords: quantum category; monoidal comonad; monoidal bicategory; quantum groupoid; bialgebroid; Hopf monoid; closed category; pseudomonoid

2000 MSC: 18D10

Theory and Applications of Categories, Vol. 24, 2010, No. 19, pp 554-563.

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