2007/11/02 by Vincent Schmitt, Schmitt, Vincent · 2 citations
Mathematics · #18D10 #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #msc:18D10 #msc:55P43
paper · pdf · doi:10.48550/arxiv.0711.0324
Improved version, with better results and better proofs
openalex publication_date 2007/11/02 · arxiv created 2008/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural transformations. Our tensor product together with a suitable unit is part of a structure on SMC that is a 2-categorical version of the symmetric monoidal closed categories. This structure is surprisingly simple. In particular the arrows involved in the associativity and symmetry laws for the tensor and in the unit cancellation laws are 2-natural and satisfy coherence axioms which are strictly commuting diagrams. We also show that the category quotient of SMC by the congruence generated by its 2-cells admits a symmetric monoidal closed structure.