Using simplicial machinery, which is analogous to that developed by Bousfield-Kan, we describe a first quadrant homotopy spectral sequence for a termwise connected pointed simplicial space X in terms of differential relations on the normalized homotopy of X and establish the existence of a smash product pairing.
Homology, Homotopy and Applications, Vol. 9 (2007), No. 2, pp.1-17.