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A Profunctorial Finiteness Semantics

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If you have a question about this talk, please contact Jean Pichon-Pharabod.

Finiteness spaces were introduced by Ehrhard as a refinement of the relational model of linear logic. A finiteness space is a set equipped with a class of finitary subsets which can be thought of being subsets that behave like finite sets. A morphism between finiteness spaces is a relation that preserves the finitary structure. This model allows for a finer analysis of the computational aspects of the relational model and it provided a semantical motivation for differential linear logic and the syntactic notion of Taylor expansion. In this talk, I will present a bicategorical generalization of this construction where the relational model is replaced with the model of generalized species of structures introduced by Fiore and the finitary property now relies on finite presentability.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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