2023/05/10 by Lukas Heidemann, Heidemann, Lukas
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Category Theory (math.CT) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic in Computer Science (cs.LO) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2305.06288
openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we extend FCT by allowing labelling systems of meshes and trusses in ∞-categories, and build an alternative model of FCT by constructing ∞-categories that classify meshes and trusses. This will serve as the foundation for future work on models of higher categories based on generalised string diagrams and the study of generalised tangles.