2015/08/31 by John Bourke, Nick Gurski
Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Cartesian tensor #Factorization #Geometric and Algebraic Topology #Gray (unit) #Homotopy and Cohomology in Algebraic Topology #Outer product #Tensor product #Tensor product of Hilbert spaces #Tensor product of algebras #math.CT #msc:18A30 #msc:18A32 #msc:18D05
paper · pdf · doi:10.1007/s10485-016-9467-6
published as Appl. Categ. Structures 25 (2017), no. 4, 603-624 · 22 pages
openalex created_date 2016/06/24 · openalex publication_date 2016/10/07 · arxiv created 2016/11/07 · arxiv updated 2022/01/31 · openalex updated_date 2026/08/05
We discuss the folklore construction of the Gray tensor product of 2-categories as obtained by factoring the map from the funny tensor product to the cartesian product. We show that this factorisation can be obtained without using a concrete presentation of the Gray tensor product, but merely its defining universal property, and use it to give another proof that the Gray tensor product forms part of a symmetric monoidal structure. The main technical tool is a method of producing new algebra structures over Lawvere 2-theories from old ones via a factorisation system.