Deriving calculus with cotriples

Authors:
B. Johnson and R. McCarthy

Journal:
Trans. Amer. Math. Soc. **356** (2004), 757-803

MSC (2000):
Primary 18G30; Secondary 55P65, 55U15

DOI:
https://doi.org/10.1090/S0002-9947-03-03318-X

Published electronically:
August 21, 2003

MathSciNet review:
2022719

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a Taylor tower for functors from pointed categories to abelian categories via cotriples associated to cross effect functors. The tower was inspired by Goodwillie's Taylor tower for functors of spaces, and is related to Dold and Puppe's stable derived functors and Mac Lane's -construction. We study the layers, , and the limit of the tower. For the latter we determine a condition on the cross effects that guarantees convergence. We define differentials for functors, and establish chain and product rules for them. We conclude by studying exponential functors in this setting and describing their Taylor towers.

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Additional Information

**B. Johnson**

Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308

Email:
johnsonb@union.edu

**R. McCarthy**

Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61801

Email:
randy@math.uiuc.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03318-X

Received by editor(s):
January 20, 1999

Received by editor(s) in revised form:
February 18, 2003

Published electronically:
August 21, 2003

Additional Notes:
The second author was supported by National Science Foundation grant # 1-5-30943 and a Sloan Fellowship

Article copyright:
© Copyright 2003
American Mathematical Society