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Bifibrations of polycategories and MLL

Banff International Research Station for Mathematical Innovation and Discovery

Polycategories are structures generalising categories and multicategories by letting both the domain and codomain of the morphisms to be lists of objects. This provides an interesting framework to study models of classical multiplicative linear logic. In particular the interpretation of the connectives ise given by objects defined by universal properties in contrast to their interpretation in a *-autonomous category. In this talk, I will introduce the notion of bifibration of polycategories and I will present how the universal properties of the connectives can be recovered as specific bifibrational properties. I will illustrate this approach through the examples of finite dimensional Banach spaces and contractive maps. These form a *-autonomous category which structure is given by lifting the compact closed structure of the category of finite dimensional vector spaces. This lifting is made possible by considering the fibrational properties of the forgetful functor between the underlying polycategories.

Mathematics; Category Theory; Homological Algebra; Algebraic Topology; Algebraic Structures

video/mp4

Author affiliation: University of Birmingham

2023-10-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86391

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/