On model structure for coreflective subcategories of a model category

Abstract

Let $\mathbf{C}$ be a coreflective subcategory of a cofibrantly generated model category $\mathbf{D}$. In this paper we show that under suitable conditions $\mathbf{C}$ admits a cofibrantly generated model structure which is left Quillen adjunct to the model structure on $\mathbf{D}$. As an application, we prove that well-known convenient categories of topological spaces, such as $k$-spaces, compactly generated spaces, and $\Delta$-generated spaces \cite{DN} (called numerically generated in \cite{KKH}) admit a finitely generated model structure which is Quillen equivalent to the standard model structure on the category $\mathbf{Top}$ of topological spaces.

6 pages

References in corpus (1)

• Homology and cohomology via enriched bifunctors