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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 TnF 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
References
Publication
Received: 27 July 2011
Revised: 7 September 2012
Accepted: 7 September 2012
Published: 18 April 2013
Authors
Rosona Eldred
Department of Mathematics
University of Hamburg
Bundesstr. 55
D-20146 Hamburg
Germany
http://www.math.uni-hamburg.de/home/eldred/