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arXiv · 1108.3376

Higher order derived functors and the Adams spectral sequence

Hans-Joachim Baues·David Blanc
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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<n+3) is a higher order Ext-group, which is determined by the track algebra of higher cohomology operations.

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Hans-Joachim Baues, David Blanc. 2011-08-17. Higher order derived functors and the Adams spectral sequence. https://arxiv.org/abs/1108.3376

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