Deriving calculus with cotriples
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- by B. Johnson and R. McCarthy PDF
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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, $D_{n}F = \operatorname {fiber}(P_{n}F\rightarrow P_{n-1}F)$, 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.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2022719