# Comparing the orthogonal and homotopy functor calculi

David Barnes, Rosona Eldred

Research output: Contribution to journalArticle

### Abstract

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.
Original language English 3650–3675 26 Journal of Pure and Applied Algebra 220 11 24 May 2016 https://doi.org/10.1016/j.jpaa.2016.05.005 Published - Nov 2016