2022/09/27 by Antonio Rieser, Rieser, Antonio · 1 citation
Mathematics · #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2209.13510
openalex publication_date 2022/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the categories PsTop and Lim of pseudotopological spaces and limit spaces, respectively, admit cofibration category structures, and that PsTop admits a model category structure, giving several ways to simultaneously study the homotopy theory of classical topological spaces, combinatorial spaces such as graphs and matroids, and metric spaces endowed with a privileged scale, in addition to spaces of maps between them. In the process, we give a sufficient condition for a topological construct which contains compactly generated Hausdorff spaces as a subcategory to admit an I-category structure. We further show that, for a topological space X∈ C, the homotopy groups of X constructed in the cofibration category on PsTop are isomorphic to those constructed classically in Top^*.