Prof. Dr. Bodo Pareigis

• Chapter 1: Toolbox
  1. Categories
  2. Functors
  3. Natural Transformations
  4. Tensor Products
  5. Algebras
  6. Coalgebras
  7. Bialgebras
  8. Representable Functors
  9. Adjoint functors and the Yoneda Lemma
  10. Limits and Colimits, Products and Equalizers
  
• Chapter 2: Commutative and Noncommutative Algebraic Geometry
  1. The Priciples of Commutative Algebraic Geometry
  2. Quantum Spaces and Noncommutative Geometry
  3. Quantum Monoids and their Actions on Quantum Spaces
  
• Chapter 3: Hopf Algebras, Algebraic, Formal, and Quantum Groups
  1. Hopf Algebras
  2. Monoids and Groups in a Category
  3. Affine Algebraic Groups
  4. Formal Groups
  5. Integrals and Fourier Transforms
  6. Quantum Groups
  7. Quantum Automorphism Groups (under construction)
  8. Duality (under construction)
  
• Chapter 4: Representation Theory and Tannaka Duality
• Chapter 5: Braidings, the Center of a Category, and the Drinfel'd Double (under construction)
• Chapter 6: The Infinitesimal Theory