Deligne-Knop tensor categories and functoriality

2024/07/04 by Inna Entova-Aizenbud, Entova-Aizenbud, Inna, Thorsten Heidersdorf +1
Mathematics · #05E05 #18D10 #20C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2407.03798

openalex publication_date 2024/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A general construction of Knop creates a symmetric monoidal category T(A,δ) from any regular category A and a fixed degree function δ. A special case of this construction are the Deligne categories \underlineRep(S_t) and \underlineRep(GL_t(\mathbbF_q)). We discuss when a functor F:A → A' between regular categories induces a symmetric monoidal functor T(A,δ) → T(A',δ'). We then give a criterion when a pair of adjoint functors between two regular categories A, A' lifts to a pair of adjoint functors between T(A,δ) and T(A',δ').

Related

• Regular categories, oligomorphic monoids, and tensor categories
• Tensor categories (after P. Deligne)
• An Introduction to Deligne Categories
• The monoidal structure on strict polynomial functors
• Inductive systems of the symmetric group, polynomial functors and tensor categories