In Calculus II, Goodwillie shows that if an S-cube X is strongly cocartesian, and X(0) --> X(s) is k_s-connected for all s, then the "product" cube X^m is k-cocartesian, where k depends on the k_s and the cardinality of S. The proof reduces to calculating the connectivity of a CW pair. Does anyone know of a more "modern" interpretation that doesn't involve this CW pair argument?

@NiallTaggart Where is that statement in the paper? And what is m?

@CharlesRezk it’s in the proof of Example 4.4, and m is just some natural number, so the “product” cube sends U to X(U)^m