Truncated derived functors and spectral sequences (Q2214746)

The \(E_2\)-term of the Adams spectral sequence [\textit{J. F. Adams}, Comment. Math. Helv. 32, 180--214 (1958; Zbl 0083.17802)] may be identified with certain derived functors, and this also holds for a number of other spectral sequences. The authors show how the higher \(E_{n+2}\)-terms for \(n\ge 0\) of such spectral sequences are determined by truncations of relative derived functors, defined in terms of certain simplicial functors called mapping algebras. The first author carried out this program for the \(E_3\)-term of the stable Adams spectral sequence in [\textit{H.-J. Baues}, The algebra of secondary cohomology operations. Basel: Birkhäuser (2006; Zbl 1091.55001)] and [\textit{H.-J. Baues} and \textit{M. Jibladze}, J. \(K\)-Theory 7, No. 2, 203--347 (2011; Zbl 1231.18009)], showing that extended calculations may be made using such a construction.