# Colloque 2016 du GDR 2875, Topologie Algébrique et Applications

11-14 October 2016
Europe/Paris timezone

## A generalized Blakers-Massey Theorem

12 Oct 2016, 15:20
50m
Amphi Lavoisier ()

### Amphi Lavoisier

Contributed talk Topologie algébrique et applications

### Speaker

Dr Georg Biedermann (LAGA, Paris 13)

### Description

(joint with M. Anel, E. Finster, and A. Joyal) We present a generalized version of the Blakers-Massey Theorem in the context of $\infty$-topoi. The proof refines a proof of the classical theorem by Finster and Lumsdaine given in the language of Homotopy Type Theory and its "re-engineered" version by Rezk. The main tools are certain factorization systems (modality) and homotopical descent. The classical theorem and a recent generalization due to Chacholski-Scherer-Werndli are easy consequences. As an application we prove a conjecture by Goodwillie: a Blakers-Massey Theorem for the calculus of homotopy functors. From it we obtain an independent proof of the fact that homogeneous functors deloop.

### Primary author

Dr Georg Biedermann (LAGA, Paris 13)

### Presentation Materials

 Transparents