Heunen, Chris;
Karvonen, Martti;
(2016)
Monads on dagger categories.
Theory and Applications of Categories
, 31
pp. 1016-1043.
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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 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.
| Type: | Article |
|---|---|
| Title: | Monads on dagger categories |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.tac.mta.ca/tac/volumes/31/35/31-35abs.h... |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Dagger category, Frobenius monad, Kleisli algebra, Eilenberg-Moore algebra |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10193414 |
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