2002/12/05 by Andrew Mauer-Oats, Mauer-Oats, Andrew
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P65
paper · pdf · doi:10.48550/arxiv.math/0212095
27 pages. Incorporates suggestions of referee, especially: more context in intro, proof that we have a cotriple is clarified, equivariant maps spelled out in detail
arxiv created 2004/02/12 · arxiv updated 2009/11/30
We define an ``algebraic'' version of the Goodwillie tower, Pnalg F(X), that depends only on the behavior of F on coproducts of X. When F is a functor to connected spaces or grouplike H-spaces, the functor Pnalg F is the base of a fibration whose fiber is the simplicial space associated to a cotriple built from the (n+1) cross effect of the functor F. When the connectivity of X is large enough (for example, when F is the identity functor and X is connected), the algebraic Goodwillie tower agrees with the ordinary (topological) Goodwillie tower, so this theory gives a way of studying the Goodwillie approximation to a functor F in many interesting cases.