  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 Chach\'olski-Scherer-Werndli. Our
proof is inspired by the one given in Homotopy Type Theory.
