2017/11/02 by Cain Edie-Michell, Edie-Michell, Cain · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1711.00645
openalex publication_date 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We further the techniques developed by Etingof, Nikshych, and Ostrik in order to classify the C-based equivalences between two G-graded extensions of C. The main result of this paper (which follows from this classification) shows that there is an action of the group Aut(G)× Aut_⊗(C) on the set of all G-graded extensions of C, and further, any two extensions in the same orbit of this action are monoidally equivalent. As a warm up for the proof of our classification result we reprove the classification of graded extensions of a fusion category, making extensive use of graphical calculus. Aside from our main result, we provide several other practical applications of our classification of C-based equivalences.