2022/02/01 by David I. Spivak, Spivak, David I.
Mathematics · #18A25 #18M05 #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.2202.00534
openalex publication_date 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this document, we collect a list of categorical structures on the category Poly of polynomial functors. There is no implied claim that this list is in any way complete. It includes: infinitely many monoidal structures, all but one of which is symmetric, closed, and distributes over +, several of which interact duoidally; it also includes a right-coclosure and two indexed left coclosures; it also includes various adjunctions of which Poly is a part, including the free monad and cofree comonad and their interaction with various monoidal structures.