On Banach spaces of sequences and free linear logic exponential modality

Abstract

We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with norms defined from pairing with finite sequences, and morphisms are bounded linear maps, continuous in a suitable topology. The main interest of the work is that our model gives a realization of the free linear logic exponentials construction.

Cited by in corpus (2)

• Linear logic in normed cones: probabilistic coherence spaces and beyond
• Lifting Coalgebra Modalities and $\mathsf{MELL}$ Model Structure to Eilenberg-Moore Categories