Monoidal Categories and Topological Field Theory

Part I. Monoidal Categories

1. Monoidal categories and functors
Vladimir Turaev, Alexis Virelizier

2. The graphical calculus
Vladimir Turaev, Alexis Virelizier

3. Braided categories
Vladimir Turaev, Alexis Virelizier

4. Fusion categories
Vladimir Turaev, Alexis Virelizier

5. The center of a monoidal category
Vladimir Turaev, Alexis Virelizier

Part II. Hopf Algebras and Monads

6. Hopf algebras in braided categories
Vladimir Turaev, Alexis Virelizier

7. Monads and bimonads
Vladimir Turaev, Alexis Virelizier

8. Hopf monads
Vladimir Turaev, Alexis Virelizier

9. Monadicity of the center
Vladimir Turaev, Alexis Virelizier

Part III. State Sum Topological Field Theory

10. Topological Quantum Field Theory
Vladimir Turaev, Alexis Virelizier

11. Skeletons of 3-manifolds
Vladimir Turaev, Alexis Virelizier

12. Multiplicity modules and colored graphs
Vladimir Turaev, Alexis Virelizier

13. The state sum TQFT
Vladimir Turaev, Alexis Virelizier

Part IV. Graph Topological Field Theory

14. Ribbon graphs in 3-manifolds
Vladimir Turaev, Alexis Virelizier

15. The state sum graph TQFT
Vladimir Turaev, Alexis Virelizier

16. Properties of the state sum graph TQFT
Vladimir Turaev, Alexis Virelizier

17. Surgery computation
Vladimir Turaev, Alexis Virelizier

Keywords: Mathematics, Category Theory, Homological Algebra, Manifolds and Cell Complexes (incl. Diff.Topology)