Secondary derived functors and the Adams spectral sequence

Hans Joachim Baues; Mamuka Jibladze

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Secondary derived functors and the Adams spectral sequence

Hans Joachim Baues·Mamuka Jibladze

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Abstract

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.

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BibTeX RIS

Hans Joachim Baues, Mamuka Jibladze. 2004-07-06. Secondary derived functors and the Adams spectral sequence. https://arxiv.org/abs/math/0407031

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