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We call attention to the intermediate constructions $\T_n F$ in Goodwillie'sCalculus of homotopy functors, giving a new model which naturally gives rise toa family of towers filtering the Taylor Tower of a functor. We also establish asurprising equivalence between the homotopy inverse limits of these towers andthe homotopy inverse limits of certain cosimplicial resolutions. Thisequivalence gives a greatly simplified construction for the homotopy inverselimit of the Taylor tower of a functor $F$ under general assumptions.

Cosimplicial models for the limit of the Goodwillie tower