A generalization of the triad theorem of Blakers-Massey
\textit{E. Dror-Farjoun} [Cellular spaces, null spaces and homotopy localization, Lect. Notes Math. 1622 (1995; Zbl 0842.55001)] gave a far-reaching generalization of cellular theory, by going from a space \(A\) to the smallest class containing \(A\), closed under weak equivalence, homotopy push-out and wedge. If \(X\) is in this class, it is said to be greater than or equal to \(A\). The author uses this to find a common generalization to the Blakers-Massey theorem [\textit{A. L. Blakers} and \textit{W. S. Massey}, Ann. Math., II. Ser. 53, 161-205 (1951; Zbl 0042.17301)] and known results comparing the homology of a space and homotopy limits. He also extends classical results of Serre relating \(H_*(E,F)\) and \(H_*(B)\) in a range of dimensions. A word of warning is appropriate. In spite of the very general language of the introduction, a space in this paper is a simplicial set.
scientific article; zbMATH DE number 1034162