Geodesic
Monads on dagger categories
Theory and applications of categories, Tome 31 (2016), pp. 1016-1043

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The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when all structure respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and its algebras should satisfy the so-called Frobenius law. Then any monad resolves as an adjunction, with extremal solutions given by the categories of Kleisli and Frobenius-Eilenberg-Moore algebras, which again have a dagger. We characterize the Frobenius law as a coherence property between dagger and closure, and characterize strong such monads as being induced by Frobenius monoids.

Publié le :
Classification : 18A40, 18C15, 18C20, 18D10, 18D15, 18D35
Keywords: Dagger category, Frobenius monad, Kleisli algebra, Eilenberg-Moore algebra 
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     author = {Chris Heunen and Martti Karvonen},
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Chris Heunen; Martti Karvonen. Monads on dagger categories. Theory and applications of categories, Tome 31 (2016), pp. 1016-1043. http://geodesic.mathdoc.fr/item/TAC_2016_31_a34/