The rank filtration and Robinson's complex

Michele Intermont, Brenda Johnson, Randy McCarthy

Research output: Contribution to journalArticle

Abstract

For a functor from the category of finite sets to abelian groups, Robinson constructed a bicomplex in [A. Robinson, Gamma homology, Lie representations and E multiplications, Invent. Math. 152 (2) (2003) 331-348] which computes the stable derived invariants of the functor as defined by Dold-Puppe in [A. Dold, D. Puppe, Homologie nicht-additiver Funktoren. Anwendungen., Ann. Inst. Fourier (Grenoble) 11 (1961) 201-312]. We identify a subcomplex of Robinson's bicomplex which is analogous to a normalization and also computes these invariants. We show that this new bicomplex arises from a natural filtration of the functor obtained by taking left Kan approximations on subcategories of bounded cardinality.

Original languageEnglish (US)
Pages (from-to)735-752
Number of pages18
JournalJournal of Pure and Applied Algebra
Volume212
Issue number4
DOIs
StatePublished - Apr 1 2008

ASJC Scopus subject areas

  • Algebra and Number Theory

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