2019/07/08 by Nicolás Cianci, Cianci, Nicolás, Miguel Ottina +1 · 1 citation
Computer Science · Mathematics · #54B30 (Secondary) #55R10 #55R15 (Primary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1907.03614
openalex publication_date 2019/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a topological variant of the Grothendieck construction which serves to represent every fiber bundle over an Alexandroff space. Using this result we give a classification theorem for fiber bundles over Alexandroff spaces with T0 fiber and we construct a universal bundle for bundles with T0 fiber over posets which are cofibrant objects of the category of small categories. Moreover, we prove that our construction induces an equivalence of categories between a suitable category of functors and the category of fiber bundles over a fixed Alexandroff space. In addition, we prove that any fiber bundle over an Alexandroff space is a fibration.