TY - JOUR
T1 - The rank filtration and Robinson's complex
AU - Intermont, Michele
AU - Johnson, Brenda
AU - McCarthy, Randy
N1 - Funding Information:
We thank the referee for his/her helpful comments. This work was supported by NSF DMS 03-06429 and the Institut Mittag-Leffler (Djursholm, Sweden).
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jpaa.2007.07.009
DO - 10.1016/j.jpaa.2007.07.009
M3 - Article
AN - SCOPUS:36148989628
SN - 0022-4049
VL - 212
SP - 735
EP - 752
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 4
ER -