TY - JOUR
T1 - Linearization, Dold-Puppe stabilization, and Mac Lane's q-construction
AU - Johnson, Brenda
AU - Mccarthy, Randy
PY - 1998
Y1 - 1998
N2 - 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.
AB - 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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U2 - 10.1090/s0002-9947-98-02067-4
DO - 10.1090/s0002-9947-98-02067-4
M3 - Article
AN - SCOPUS:22044450160
SN - 0002-9947
VL - 350
SP - 1555
EP - 1593
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 4
ER -