Higher order derived functors and the Adams spectral sequence
Algebraic Topology
2014-05-02 v2 Category Theory
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.
Cite
@article{arxiv.1108.3376,
title = {Higher order derived functors and the Adams spectral sequence},
author = {Hans-Joachim Baues and David Blanc},
journal= {arXiv preprint arXiv:1108.3376},
year = {2014}
}
Comments
To appear in J. Pure & Appl. Algebra