Brenda Johnson - Constructing and characterizing degree n functors

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Brenda Johnson - Constructing and characterizing degree n functors

BRENDA JOHNSON, Department of Mathematics, Union College, Schenectady, New York 12308, USA

Constructing and characterizing degree n functors

Let F be a functor from a basepointed category with finite coproducts to a category of chain complexes over an abelian category. Such a functor is homologically degree n if its n+1-st cross effect (in the sense of Eilenberg and Mac Lane) has trivial homology. We describe a method for constructing, by means of cotriples associated to the cross effects of F, a universal tower under F,

$\begin{displaymath}\cdots \rightarrow P_{n+1}F\rightarrow P_nF\rightarrow P_{n-1}F\rightarrow \cdots \rightarrow P_1F\rightarrow P_0F=F(\ast), \end{displaymath}$

in which each functor P_nF is homologically degree n. This construction arose from the study of Goodwillie's Taylor tower in the case of functors of modules over a ring. Using this model, we will characterize homologically degree n functors in terms of modules over a certain DGA, and discuss some related constructions and examples due to Eilenberg-Mac Lane, and Dold-Puppe. This is joint work with Randy McCarthy.

Next: Keith Johnson - Elliptic Up: 2) Homotopy Theory / Théorie Previous: Barry Jessup - Estimating