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

Brenda Johnson, Randy Mccarthy

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1555-1593
Number of pages39
JournalTransactions of the American Mathematical Society
Issue number4
StatePublished - 1998

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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