2021/07/06 by Kevin Coulembier, Coulembier, Kevin · 3 citations
Mathematics · #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.2107.02374
openalex publication_date 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that each rigid monoidal category A over a field defines a family of universal tensor categories, which together classify all faithful monoidal functors from A to tensor categories. Each of the universal tensor categories classifies monoidal functors of a given 'homological kernel' and can be realised as a sheaf category, not necessarily on A. This yields a theory of 'local abelian envelope' which completes the notion of monoidal abelian envelopes.