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A linear category of polynomial diagrams

Published online by Cambridge University Press:  17 May 2013

PIERRE HYVERNAT
PIERRE HYVERNAT*
Affiliation:
Laboratoire de Mathématiques, CNRS UMR 5126 – Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France Email: pierre.hyvernat@univ-savoie.fr Website: http://lama.univ-savoie.fr/~hyvernat/
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Abstract

We present a categorical model for intuitionistic linear logic in which objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally cartesian closed category, but the additive (product and coproduct) and exponential (-comonoid comonad) structures require additional properties and are only developed in the category Set, where the objects and morphisms have natural interpretations in terms of games, simulation and strategies.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 1 , February 2014 , e240104
Copyright
Copyright © Cambridge University Press 2013 

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