Open Collections

Functor calculus

Banff International Research Station for Mathematical Innovation and Discovery

Functor calculus is a way of organizing the interplay between homotopy theory and stable homotopy theory. Its name reflects an analogy with differential calculus. There are derivatives, $n$th derivatives, and Taylor polynomials in functor calculus. Functors between homotopical categories (categories which, like the category of topological spaces, have a suitable structure for â doing homotopy theoryâ ) can be thought of as resembling smooth maps between manifolds. Homotopical categories that are stable correspond to manifolds that are vector spaces. I will sketch the high points of functor calculus with this geometric analogy in mind. Until recently the relation with smooth geometry has existed mostly as a suggestive analogy. It is being pursued in detail now by Bauer, Burke, Ching, and others using the framework of tangent structures on categories.

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

video/mp4

Author affiliation: Brown University

2023-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86379

Unreviewed

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