A generalized Blakers-Massey theorem

(joint with M. Anel, E. Finster, and A. Joyal) We present a generalization of the Blakers-Massey theorem for higher topoi. The main tool are "modalities", unique factorization systems whose left class is closed under homotopy base change. As an application we prove a Blakers-Massey type theorem for the Goodwillie tower of a homotopy functor.