Goodwillie's calculus of functors and higher topos theory
| Autor: | André Joyal, Eric Finster, Georg Biedermann, Mathieu Anel |
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| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Pure mathematics Functor Calculus of functors 010102 general mathematics Pushout Type (model theory) Mathematics::Algebraic Topology 01 natural sciences Tower (mathematics) Topos theory Mathematics::K-Theory and Homology Mathematics::Category Theory Product (mathematics) 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Journal of Topology. 11:1100-1132 |
| ISSN: | 1753-8416 |
| DOI: | 10.1112/topo.12082 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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