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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Linearization, Dold-Puppe stabilization, and Mac Lane’s $Q$-construction
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by Brenda Johnson and Randy McCarthy PDF
Trans. Amer. Math. Soc. 350 (1998), 1555-1593 Request permission


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:
  • Randy McCarthy
  • Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
  • Email:
  • Received by editor(s): July 16, 1996
  • Additional Notes: This work was supported by National Science Foundation grant # 1-5-30943.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 1555-1593
  • MSC (1991): Primary 18G99, 18E25, 55P65, 55U99
  • DOI:
  • MathSciNet review: 1451606