A second quadrant homotopy spectral sequence

Abstract

For each cosimplicial simplicial set with basepoint, the authors construct a homotopy Spectral sequence generalizing the usual spectral sequence for a second quadrant double chain complex. For such homotopy spectral sequences, a uniqueness theorem and a general multiplicative pairing are established. This machinery is used elsewhere to show the equivalence of various unstable Adams spectral sequences and to construct for them certain composition pairings and Whitehead products.