The course notes were prepared jointly by Prof. Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik.
The book Tensor Categories based on these 2009 notes was published by the American Mathematical Society in 2015. A complete file of the book (PDF - 3.1MB) is on Prof. Etingof’s webpage. [Please note: This file cannot be posted on any website not belonging to the authors.]
Complete 2009 lecture notes in one file (PDF - 2.5MB)
| 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) |
