| SES # | TOPICS | LECTURE NOTES |
|---|---|---|
| 1 | Basics of monoidal categories | (PDF) |
| 2 |
Monoidal functors MacLane's strictness theorem |
(PDF) |
| 3 |
MacLane coherence theorem Rigid monoidal categories Invertible objects Tensor and multitensor categories |
(PDF) |
| 4 |
Tensor product and tensor functors Unit object Grothendieck rings Groupoids Finite abelian categories Fiber functors Coalgebras |
(PDF) |
| 5 | Bialgebras and Hopf algebras | (PDF) |
| 6 |
Quantum groups Skew-primitive elements Pointed tensor categories Coradical filtration Chevalley's theorem and Chevalley property |
(PDF) |
| 7 |
Andruskeiwitsch-Schneider conjecture Cartier-Kostant theorem Quasi-bialgebras and quasi-Hopf algebras |
(PDF) |
| 8 |
Quantum traces Pivotal categories and dimensions Spherical categories Multitensor cateogries Multifusion rings Frobenius-Perron theorem |
(PDF) |
| 9 |
Tensor categories Deligne's tensor product Finite (multi)tensor categories Categorical freeness |
(PDF) |
| 10 |
Distinguished invertible object Integrals in quasi-Hopf algebras Cartan matrix Basics of Module categories |
(PDF) |
| 11 |
Exact module categories Algebras in categories Internal Hom |
(PDF) |
| 12 |
Main Theorem Categories of module functors Dual categories |
(PDF) |
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