Lecture Notes

The course notes were prepared jointly by Prof. Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik.

Complete lecture notes (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)