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) |