Descent and forms of tensor categories

2011/02/03 by Pavel Etingof, Shlomo Gelaki, Etingof, Pavel +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1102.0657

openalex publication_date 2011/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of forms. We also discuss the problem of categorification of weak fusion rings, and for the simplest families of such rings, determine which ones are categorifiable.

Cited by

• Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

Related

• Modular tensor categories, subcategories, and Galois orbits
• Examples of categorification
• Lifting (co)stratifications between tensor triangulated categories
• Finite tensor categories
• Homological stratification and descent