A Linear Category of Polynomial Functors (extensional part)

Pierre Hyvernat (1)

1 LAMA - Laboratoire de Mathématiques

We construct a symmetric monoidal closed category of //polynomial endofunctors// (as objects) and //simulation cells// (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is reminiscent of Day's convolution on presheaves. We then make this category into a model for intuitionistic linear logic by defining an additive and exponential structure.

Mots clés: polynomial functors; linear logic; Day convolution

Domaines: Logique en informatique [cs.LO]

Pierre Hyvernat. A Linear Category of Polynomial Functors (extensional part). 2013. ⟨hal-00955307v3⟩