2024/07/18 by Jonte Gödicke, Gödicke, Jonte
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2407.13357
openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Algebra objects in ∞-categories of spans admit a description in terms of 2-Segal objects. We introduce a notion of span between 2-Segal objects and extend this correspondence to an equivalence of ∞-categories. Additionally, for every ∞-category with finite limits C, we introduce a notion of a birelative 2-Segal object in C and establish a similar equivalence with the ∞-category of bimodule objects in spans. Examples of these concepts arise from algebraic and hermitian K-theory through the corresponding Waldhausen S\bullet-construction. Apart from their categorical relevance, these concepts can be used to construct homotopy coherent representations of Hall algebras.