A Generalized Blakers-Massey Theorem

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.