Linearization, DoldPuppe stabilization, and Mac Lane's construction
Authors:
Brenda Johnson and Randy McCarthy
Journal:
Trans. Amer. Math. Soc. 350 (1998), 15551593
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 quasiisomorphism, 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 DoldPuppe stabilization and Mac Lane's 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/S0002994798020674
PII:
S 00029947(98)020674
Received by editor(s):
July 16, 1996
Additional Notes:
This work was supported by National Science Foundation grant # 1530943.
Article copyright:
© Copyright 1998 American Mathematical Society
