In order to prepare for class, students are required to read selections from the course notes. These readings can be found on the lecture notes page.
| SES # | TOPICS | READINGS |
|---|---|---|
| 1 | Basics of monoidal categories | Sections 1.1-1.3 |
| 2 |
Monoidal functors MacLane’s strictness theorem |
Sections 1.4-1.8 |
| 3 |
MacLane coherence theorem Rigid monoidal categories Invertible objects Tensor and multitensor categories |
Sections 1.9-1.12 |
| 4 |
Tensor product and tensor functors Unit object Grothendieck rings Groupoids Finite abelian categories Fiber functors Coalgebras |
Sections 1.13-1.20 |
| 5 | Bialgebras and Hopf algebras | Sections 1.21-1.24 |
| 6 |
Quantum groups Skew-primitive elements Pointed tensor categories Coradical filtration Chevalley’s theorem and Chevalley property |
Sections 1.25-1.31 |
| 7 |
Andruskeiwitsch-Schneider conjecture Cartier-Kostant theorem Quasi-bialgebras and quasi-Hopf algebras |
Sections 1.32-1.36 |
| 8 |
Quantum traces Pivotal categories and dimensions Spherical categories Multitensor cateogries Multifusion rings Frobenius-Perron theorem |
Sections 1.37-1.44 |
| 9 |
Tensor categories Deligne’s tensor product Finite (multi)tensor categories Categorical freeness |
Sections 1.45-1.50 |
| 10 |
Distinguished invertible object Integrals in quasi-Hopf algebras Cartan matrix Basics of Module categories |
Sections 1.51-1.53 and 2.1-2.6 |
| 11 |
Exact module categories Algebras in categories Internal Hom |
Sections 2.7-2.10 |
| 12 |
Main Theorem Categories of module functors Dual categories |
Sections 2.11-2.14 |
