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Goodwillie's calculus of functors and higher topos theory

2018; Wiley; Volume: 11; Issue: 4 Linguagem: Inglês

10.1112/topo.12082

1753-8424

Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal,

Algebraic structures and combinatorial models

We develop an approach to Goodwillie's calculus of functors using the techniques of higher topos theory. Central to our method is the introduction of the notion of fiberwise orthogonality, a strengthening of ordinary orthogonality which allows us to give a number of useful characterizations of the class of n-excisive maps. We use these results to show that the pushout product of a P n -equivalence with a P m -equivalence is a P m + n + 1 -equivalence. Building on topos-theoretic methods developed in previous work, we then prove a Blakers–Massey type theorem for the Goodwillie tower of functors. We show how to use the resulting techniques to rederive some foundational theorems in the subject, such as delooping of homogeneous functors.