A Generalized Blakers-Massey Theorem

Abstract

We prove a generalization of the classical connectivity theorem of Blakers-Massey, valid in an arbitrary higher topos and with respect to an arbitrary modality, that is, a factorization system (L,R) in which the left class is stable by base change. We explain how to rederive the classical result, as well as a recent generalization by Chachólski-Scherer-Werndli. Our proof is inspired by the one given in Homotopy Type Theory.

v5: few typos corrected, 38 pages, paper accepted for publication in the Journal of Topology

References in corpus (2)

• Goodwillie's Calculus of Functors and Higher Topos Theory
• Small object arguments, plus-construction, and left-exact localizations

Cited by in corpus (7)

• Left-exact Localizations of $\infty$-Topoi I: Higher Sheaves
• Modal Fracture of Higher Groups
• Filter Quotients and Non-Presentable $(\infty ,1)$-Toposes
• Smooth generalized symmetries of quantum field theories
• Left-exact Localizations of $\infty$-Topoi III: The Acyclic Product
• Epimorphisms and Acyclic Types in Univalent Foundations
• Smooth and Proper Maps