Linearization, Dold-Puppe stabilization,

and Mac Lane's -construction

Authors:
Brenda Johnson and Randy McCarthy

Journal:
Trans. Amer. Math. Soc. **350** (1998), 1555-1593

MSC (1991):
Primary 18G99, 18E25, 55P65, 55U99

DOI:
https://doi.org/10.1090/S0002-9947-98-02067-4

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 -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:
https://doi.org/10.1090/S0002-9947-98-02067-4

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