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arXiv · 1703.09632

Goodwillie's Calculus of Functors and Higher Topos Theory

Mathieu Anel·Georg Biedermann·Eric Finster·André Joyal
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Abstract

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. Then, building on our previous work, we prove a Blakers-Massey type theorem for the Goodwillie tower. We show how to use the resulting techniques to rederive some foundational theorems in the subject, such as delooping of homogeneous functors.

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Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal. 2017-03-28. Goodwillie's Calculus of Functors and Higher Topos Theory. https://doi.org/10.1112/topo.12082

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