Monads on Dagger Categories

Christiaan Heunen, Martti Karvonen

Research output: Contribution to journalArticlepeer-review

Abstract

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 FrobeniusEilenberg-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.
Original languageEnglish
Pages (from-to)1016-1043
Number of pages29
JournalTheory and Applications of Categories
Volume31
Issue number35
Publication statusPublished - 7 Nov 2016

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