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Colloque 2016 du GDR 2875, Topologie Algébrique et Applications

11-14 octobre 2016
Europe/Paris timezone
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Contribution Contributed talk

Topologie algébrique et applications

A generalized Blakers-Massey Theorem

Intervenant(s)

• Dr. Georg BIEDERMANN

Content

(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.