Functor calculus via non-cubes
Algebraic Topology
2025-05-08 v2 Category Theory
Abstract
We study versions of Goodwillie's calculus of functors for indexing diagrams other than cubes. We in particular construct universal excisive approximations for a larger class of diagrams, which yields an extension of the Taylor tower. We prove that the limit of this extension agrees with the limit of the Taylor tower using criteria for the existence of maps between excisive approximations. Lastly we investigate in which cases our new notions of excision coincide with classical ones.
Cite
@article{arxiv.2205.15880,
title = {Functor calculus via non-cubes},
author = {Robin Stoll},
journal= {arXiv preprint arXiv:2205.15880},
year = {2025}
}
Comments
82 pages. v2: Minor changes after referee report; published version