2017/08/16 by Jonathan E. Rubin, Rubin, Jonathan
Mathematics · Medicine · #55P91 (Primary) 18D10 (Secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracerebral and Subarachnoid Hemorrhage Research
paper · pdf · doi:10.48550/arxiv.1708.04777
openalex publication_date 2017/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce categorical models of N_∞ spaces, which we call normed symmetric monoidal categories (NSMCs). These are ordinary symmetric monoidal categories equipped with compatible families of norm maps, and when specialized to a particular class of examples, they reveal a connection between the equivariant symmetric monoidal categories of Guillou-May-Merling-Osorno and those of Hill-Hopkins. We also give an operadic interpretation of the Mac Lane coherence theorem and generalize it to include NSMCs. Among other things, this theorem ensures that the classifying space of a NSMC is a N_∞ space. We conclude by extending our coherence theorem to include NSMCs with strict relations.