From: tchernev@math.albany.edu
Date: Thu Sep 28 21:51:49 EDT 2000
Newsgroups: capdist.seminars,sunya.cs.general
Subject: next CRANTS
Organization: Dept of Math & Stat, The University at Albany
Reply-To: mathdept@math.albany.edu




Dear Colleagues, 

The speaker and title for the next CRANTS talk are: 

Speaker:  Professor Brenda Johnson 
Title  :  Constructing and Characterizing Degree $n$ Functors
Time   :  Wed, Oct 4, 4:30pm, in ES 152A   

Abstract: 

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,
$$
\dots \rightarrow P_{n+1}F\rightarrow P_nF\rightarrow P_{n-1}F\rightarrow
\dots \rightarrow P_1F\rightarrow P_0F=F(*),
$$
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  due to Eilenberg-Mac
Lane, and Dold-Puppe.  (This is joint work with Randy McCarthy.)



Refreshments will be served at 4:20pm in ES 152. 

Alex Tchernev