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arXiv · 1602.04324

Monads on dagger categories

Chris Heunen·Martti Karvonen
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Abstract

The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when everything 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.

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Chris Heunen, Martti Karvonen. 2016-02-13. Monads on dagger categories. https://doi.org/10.70930/tac/kvbpoc6x

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