An algebraic model of the Leray spectral sequence (Q2711883)

In this well written article the author using his notion of generalized differential forms over operads [ibid. 329, No. 11, 939--942 (1999; Zbl 0937.55008)] constructs a Leray type spectral sequence for a surjective map between simplicial sets. The construction is inspired by earlier work of [\textit{P.-P. Grivel}, Ann. Inst. Fourier 29, No. 3, 17--37 (1979; Zbl 0381.55008)] in the context of simplicial de Rham theory and minimal models. In the special case that the map is actually a Kan fibration and the base is connected with a simple system of local coefficients he recovers the Leray-Serre type spectral sequence of a fibration. As an interesting application of such a Leray-Serre spectral sequence associated to generalized differential forms for \(E_\infty\) algebras, he is able to determine the algebraic model of the fiber of a simplicial map, a question also arising in the context of the work of \textit{M. A. Mandell} on \(p\)-adic homotopy theory [Topology 40, No. 1, 43--94 (2001; Zbl 0974.55004)].