Open Collections

Tangent Infinity Categories

Banff International Research Station for Mathematical Innovation and Discovery

This is joint work with M. Burke and M. Ching. In this talk, I will present the definition of a tangent infinity category as a generalization of Leung's presentation of tangent categories as Weil-modules. A key example of a tangent structure on the infinity category of infinity categories is an extension of Lurieâ s tangent bundle functor. We call this the Goodwillie tangent structure, since it encodes the theory of Goodwillie calculus. The differential objects in this tangent infinity category are precisely the stable infinity categories. Following Cockett-Cruttwell these form a cartesian differential category. I will explain that the derivative in this CDC is the same as the BJORT derivative for abelian functor calculus, showing that the Goodwillie tangent structure is an extension of BJORT.

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

video/mp4

Author affiliation: University of Calgary

2023-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86381

Unreviewed

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