Exercises can be found in the lecture notes.
| SES # | TOPICS | ASSIGNMENTS |
|---|---|---|
| 1 | Basics of monoidal categories | Exercise 1.2.5 |
| 2 |
Monoidal functors MacLane’s strictness theorem |
Exercises 1.4.4, 1.7.5, 1.8.8 |
| 3 |
MacLane coherence theorem Rigid monoidal categories Invertible objects Tensor and multitensor categories |
Exercises 1.10.5, 1.10.6, 1.10.8, 1.10.15, 1.10.16 |
| 4 |
Tensor product and tensor functors Unit object Grothendieck rings Groupoids Finite abelian categories Fiber functors Coalgebras |
Exercises 1.15.3, 1.15.6, 1.15.10, 1.17.1, 1.17.3, 1.18.3, 1.19.3, 1.20.3, 1.20.4 |
| 5 | Bialgebras and Hopf algebras | Exercises 1.21.4, 1.21.5, 1.21.6, 1.22.3, 1.22.12, 1.22.14, 1.22.16, 1.22.17, 1.22.18, 1.24.3, 1.24.4, 1.24.8, 1.24.10, 1.24.11 |
| 6 |
Quantum groups Skew-primitive elements Pointed tensor categories Coradical filtration Chevalley’s theorem and Chevalley property |
Exercises 1.25.3, 1.29.2, 1.31.7 |
| 7 |
Andruskeiwitsch-Schneider conjecture Cartier-Kostant theorem Quasi-bialgebras and quasi-Hopf algebras |
Exercises 1.34.9, 1.35.3, 1.36.3 |
| 8 |
Quantum traces Pivotal categories and dimensions Spherical categories Multitensor cateogries Multifusion rings Frobenius-Perron theorem |
Exercises 1.37.2, 1.27.4, 1.38.3, 1.39.3, 1.42.7 |
| 9 |
Tensor categories Deligne’s tensor product Finite (multi)tensor categories Categorical freeness |
Exercises 1.45.14, 1.49.2 |
| 10 |
Distinguished invertible object Integrals in quasi-Hopf algebras Cartan matrix Basics of Module categories |
Exercises 1.52.9, 2.1.4, 2.1.7, 2.5.3, 2.5.8, 2.6.2, 2.6.7 |
| 11 |
Exact module categories Algebras in categories Internal Hom |
Exercises 2.8.2, 2.8.4, 2.8.6, 2.8.8, 2.9.7, 2.9.8, 2.9.9, 2.9.11, 2.9.13, 2.9.13, 2.9.15, 2.9.16, 2.9.17, 2.9.20, 2.9.23, 2.9.26, 2.10.3, 2.10.9 |
| 12 |
Main Theorem Categories of module functors Dual categories |
Exercises 2.11.1, 2.11.4, 2.11.5, 2.12.4, 2.13.1 |
