Higher order derived functors and the Adams spectral sequence

2011/08/17 by Baues, Hans-Joachim, Blanc, David
#55S20 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Primary: 18G10 #secondary: 55T15

paper · doi:10.48550/arxiv.1108.3376

Abstract

Classical homological algebra considers chain complexes, resolutions, and derived functors in additive categories. We describe "track algebras in dimension n", which generalize additive categories, and we define higher order chain complexes, resolutions, and derived functors. We show that higher order resolutions exist in higher track categories, and that they determine higher order Ext-groups. In particular, the E_m-term of the Adams spectral sequence (m

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