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Relative pseudomonads

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It is well-known that monads admit an equivalent presentation via the notion of a Kleisli triple. In recent work, Altenkirch, Chapman and Uustalo generalized Kleisli triples to what they call relative monads, avoiding the assumption that the functor part of the monad is an endofunctor. In this talk, I will present the corresponding 2-categorical notion, that of relative pseudomonad, and offer some applications. In particular, I will show how the presheaf construction gives rise in a natural way to a relative pseudomonad, how this allows us to see the bicategory of profunctors as a Kleisli bicategory, and illustrate how this gives rise to a 2-categorical version of the relational model of linear logic. This is joint work with M. Fiore, M. Hyland, and G. Winskel.

This talk is part of the Theoretical computer science seminar series.

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