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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: August 21, 2003
MathSciNet review: 2022719
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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 $Q$-construction. We study the layers, $D_{n}F=\text{\rm fiber}(P_{n}F\rightarrow P_{n-1}F)$, 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: http://dx.doi.org/10.1090/S0002-9947-03-03318-X
PII: S 0002-9947(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