Homotopy limits of categories
Given a diagram \(A : {\mathcal I} \to {\mathcal C}at\) of small categories, \textit{R. W. Thomason} [Math. Proc. Cambridge Philos. Soc. 85, 91-109 (1979; Zbl 0392.18001)] proved that the Grothendieck construction \({\mathcal I} \int A\) is a category with nerve homotopically equivalent to hocolim NA, the homotopy colimit of NA, the corresponding diagram of simplicial sets obtained by applying the nerve to \(A\). Considering holim NA, the homotopy limit of \(A\), the author proves that it is isomorphic to the nerve of a category and uses this to prove a weak form of the Bousfield-Kan cofinality theorem.
scientific article; zbMATH DE number 719443