Open Collections

From categorical models of differentiation to topologies in vector spaces.

Banff International Research Station for Mathematical Innovation and Discovery

Differential categories have a rich relation with proof theory and linear logic. In this talk, we will focus on models interpreting differential linear logic in topological vector spaces, and specifically for models interpreting the involutive linear negation of classical linear logic. We will survey the main ingredients that can make a category with smooth functions over topological vector spaces cartesian closed. We also review the main limitations to reaching *-autonomy in topological vector spaces. If time permits, we will explore how chiralities, models of polarized linear logic, are especially appropriate in this context, and facilitate the search for cartesian closedness and *-autonomy.

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

video/mp4

Author affiliation: LIPN, CNRS, Université Sorbonne Paris Nord

2023-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86385

Unreviewed

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