A generalized Blakers–Massey theorem. Issue 4 (7th September 2020)

• Record Type: Journal Article
• Authors: Anel, Mathieu; Biedermann, Georg; Finster, Eric; Joyal, André
• Is Part Of: Journal of topology. Volume 13:Issue 4(2020)
• Page Start: 1521
• Page End: 1553
• Publication Date: 2020-09-07
• Subjects: 55P99 (primary) -- 18F99 -- 18B25 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12163
• Languages: English
• ISSNs: 1753-8416

Abstract

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 the recent generalization of Chachólski, Scherer and Werndli ( Ann. Inst. Fourier 66 (2016) 2641–2665). Our proof is inspired by the one given in homotopy‐type theory in Favonia et al . (2016).