Eric Finster: The Generalized Blakers-Massey Theorem

I will describe a generalization of the classical Blakers-Masssey theorem to the setting of what I call a factorization hierarchy in an arbitrary infinity-topos E.  This consists of an N-indexed family of factorization systems on E satisfying some compatibility conditions and finite generation hypotheses.  Applied to the factorization systems consisting of n-truncated and n-connected maps, we recover the classical Blakers-Massey theorem.  Moreover, we sketch a proof  of the fact that the factorzation systems of n-excisive and n-reduced maps in the Goodwillie calculus also satisfy these axioms, proving a conjecture of Goodwillie.