2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148421We define a closed model category containing the $n$-nerves defined by Tamsamani, and admitting internal $Hom$. This allows us to construct the $n+1$-category $nCAT$ by taking the internal $Hom$ for fibrant objects. We prove a generalized Seifert-Van Kampen theorem for Tamsamani's Poincaré $n$-groupoid of a topological space. We give a still-speculative discussion of $n$-stacks, and similarly of comparison with other possible definitions of $n$-category.Corrects an error in the proof of Theorem 5.1, by rewriting locally. Doesn't change the rest of the text, so numerous expositional problems are left untouchedAlgebraic GeometryQuantum Algebratext