Volume 13, issue 2 (2013)

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Cosimplicial models for the limit of the Goodwillie tower

Rosona Eldred

Algebraic & Geometric Topology 13 (2013) 1161–1182
Abstract

We call attention to the intermediate constructions ${T}_{n}F$ in Goodwillie’s Calculus of homotopy functors, giving a new model which naturally gives rise to a family of towers filtering the Taylor tower of a functor. We also establish a surprising equivalence between the homotopy inverse limits of these towers and the homotopy inverse limits of certain cosimplicial resolutions. This equivalence gives a greatly simplified construction for the homotopy inverse limit of the Taylor tower of a functor $F$ under general assumptions.

Keywords
cosimplicial, Goodwillie Calculus, homotopy functor, homotopy limit, cofinal
Mathematical Subject Classification 2010
Primary: 55P65, 55P60
Secondary: 55P10