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

 

Linearization, Dold-Puppe stabilization,
and Mac Lane's $Q$-construction


Authors: Brenda Johnson and Randy McCarthy
Journal: Trans. Amer. Math. Soc. 350 (1998), 1555-1593
MSC (1991): Primary 18G99, 18E25, 55P65, 55U99
MathSciNet review: 1451606
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Abstract: In this paper we study linear functors, i.e., functors of chain complexes of modules which preserve direct sums up to quasi-isomorphism, in order to lay the foundation for a further study of the Goodwillie calculus in this setting. We compare the methods of Dold and Puppe, Mac Lane, and Goodwillie for producing linear approximations to functors, and establish conditions under which these methods are equivalent. In addition, we classify linear functors in terms of modules over an explicit differential graded algebra. Several classical results involving Dold-Puppe stabilization and Mac Lane's $Q$-construction are extended or given new proofs.


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Additional Information

Brenda Johnson
Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308
Email: johnsonb@union.edu

Randy McCarthy
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: randy@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02067-4
PII: S 0002-9947(98)02067-4
Received by editor(s): July 16, 1996
Additional Notes: This work was supported by National Science Foundation grant # 1-5-30943.
Article copyright: © Copyright 1998 American Mathematical Society