Pivotal Objects in Monoidal Categories and Their Hopf Monads

zbMath1458.18009arXiv2005.07183MaRDI QIDQ5858941

Aryan Ghobadi

Publication date: 15 April 2021

Full work available at URL: https://arxiv.org/abs/2005.07183

zbMATH Keywords

Hopf algebramonoidal categorytensor categorypivotal categoryclosed categoryHopf monad

Mathematics Subject Classification ID

Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) Eilenberg-Moore and Kleisli constructions for monads (18C20) Hopf algebras, quantum groups and related topics (16T99) Monoidal categories, symmetric monoidal categories (18M05)

Related Items (2)

Isotropy quotients of Hopf algebroids and the fundamental groupoid of digraphs ⋮ Hopf monads: a survey with new examples and applications

Cites Work

• The dual and the double of a Hopf algebroid are Hopf algebroids
• Hopf monads on monoidal categories
• Frobenius-Schur indicators and exponents of spherical categories.
• Hopf comonads on naturally Frobenius map-monoidales
• The monoidal Eilenberg-Moore construction and bialgebroids
• Hopf algebras and their generalizations from a category theoretical point of view
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Hopf algebroids with bijective antipodes: axioms, integrals, and duals.
• The pivotal cover and Frobenius-Schur indicators
• Monoidal categories and topological field theory
• Hopf monads
• Quantum double of Hopf monads and categorical centers
• Exact Sequences of Tensor Categories
• Tensor Categories
• Monads on tensor categories
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