2025/05/14 by Yifan Li, Li, Yifan · 1 citation
Social Sciences · #18N60 #55P42 #Algebraic Topology (math.AT) #Classical Antiquity Studies #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2505.09150
openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we give an introduction to the notion of ambidexterity and norm map, and construct inductively the canonical norm map for m-truncated maps for some m≥-1, on which the definitions of integration and cardinality are built. We then use several propositions to justify the properties of cardinality and integration and their compatibility with monoidal structure. We give a brief introduction of the definition and behaviors of semiadditive height. Focusing on stable monoidal p-local ∞-categories of height 1, for any finite group G, with the help of Möbius function and Burnside ring, we give an explicit decomposition of the cardinality of BG into an expression of the cardinality of BCp. Eventually, we generalize the result and conclude with a formula of the cardinality of any π-finite space A.