2023/05/04 by Brandon T. Shapiro, Lynch, Owen, David I. Spivak +2
Mathematics · #18A05 #18A35 #18B10 #18B15 #18B20 #18D15 #18M05 #18M35 #68Q70 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2305.02571
openalex publication_date 2023/05/04 · openalex created_date 2023/05/07 · openalex updated_date 2026/07/28
We show that the double category ℂat^# of comonoids in the category of polynomial functors (previously shown by Ahman-Uustalu and Garner to be equivalent to the double category of categories, cofunctors, and prafunctors) contains several formal settings for basic category theory and has subcategories equivalent to both the double category \mathbbOrg of dynamic rewiring systems and the double category ℙolyE of generalized polynomials in a finite limit category E. Also serving as a natural setting for categorical database theory and generalized higher category theory, ℂat^# at once hosts models of a wide range of concepts from the theory and applications of polynomial functors and category theory.