A Linear Category of Polynomial Diagrams

Pierre Hyvernat (1)

1 LAMA - Laboratoire de Mathématiques

We present a categorical model for intuitionistic linear logic where 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, whereas the additive (product and coproduct) and exponential Tensor-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.

Mots clés: polynomial functors; linear logic

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Pierre Hyvernat. A Linear Category of Polynomial Diagrams. Mathematical Structures in Computer Science, 2014, 24 (1), pp.e240104. ⟨10.1017/S0960129512001016⟩. ⟨hal-00728259⟩