arXiv:1108.3376 Higher order derived functors and the Adams spectral sequence from arXiv Front: math.CT by Hans-Joachim Baues, David Blanc 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 less than n+3) is a higher order Ext-group, which is determined by the track algebra of higher cohomology operations.
nLab page on Track category