2009/10/03 by Dimitri Chikhladze, Chikhladze, Dimitri
Mathematics · #18D35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0910.0512
openalex publication_date 2009/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set of axioms close to the definitions of a bialgebroid in the Hopf algebraic literature. We define notions of functor and natural transformation for quantum categories.