Secondary derived functors and the Adams spectral sequence

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Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of ``additive groupoid enriched categories'', in which a secondary analog of homological algebra can be performed. We introduce secondary chain complexes and secondary resolutions leading to the concept of secondary derived functors. As a main result we show that the E_3-term of the Adams spectral sequence can be expressed as a secondary derived functor. This result can be used to compute the E_3-term explicitly by an algorithm.
Reference to math.AT/0407045 added

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Algebraic Topology, Category Theory, K-Theory and Homology, 18G10, 55T15, 55S20 (Primary) 55U99, 18D05, 18G25, 18G40 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/71760

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407031
 http://arxiv.org/abs/math/0407031

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arXiv