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Universal algebra over nominal sets

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We investigate the foundations of a theory of algebraic data types with variable binding inside classical many-sorted universal algebra. The nominal sets introduced by Gabbay and Pitts give an elegant treatment of abstract syntax with binders. This talk presents a category-theoretic study of monads over nominal sets that leads us to introduce new notions of finitary based monads and uniform monads. The close connection between nominal sets and the presheaf category [I,Set] enables us to spell out these notions in the language of universal algebra. We show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and how to transfer classical results from universal algebra to nominal sets.

This is joint work with Alexander Kurz (University of Leicester) and JirĂ­ Velebil (Czech Technical University, Prague).

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

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