On Köthe Sequence Spaces and Linear Logic

We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Köthe sequence spaces. In this setting, the “of course” connective of linear logic has a quite simple structure of commutative Hopf algebra. The co-Kleisli category of this linear category is a cartesian closed category of entire mappings. This work provides a simple setting where typed λ-calculus and differential calculus can be combined; we give a few examples of computations.