Secondary derived functors and the Adams spectral sequence

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 E₃-term of the Adams spectral sequence can be expressed as a secondary derived functor. This result can be used to compute the E₃-term explicitly by an algorithm.