# Assignments

Exercises can be found in the lecture notes.

SES # TOPICS ASSIGNMENTS
1 Basics of monoidal categories Exercise 1.2.5
2

Monoidal functors

MacLane's strictness theorem

Exercises 1.4.4, 1.7.5, 1.8.8
3

MacLane coherence theorem

Rigid monoidal categories

Invertible objects

Tensor and multitensor categories

Exercises 1.10.5, 1.10.6, 1.10.8, 1.10.15, 1.10.16
4

Tensor product and tensor functors

Unit object

Grothendieck rings

Groupoids

Finite abelian categories

Fiber functors

Coalgebras

Exercises 1.15.3, 1.15.6, 1.15.10, 1.17.1, 1.17.3, 1.18.3, 1.19.3, 1.20.3, 1.20.4
5 Bialgebras and Hopf algebras Exercises 1.21.4, 1.21.5, 1.21.6, 1.22.3, 1.22.12, 1.22.14, 1.22.16, 1.22.17, 1.22.18, 1.24.3, 1.24.4, 1.24.8, 1.24.10, 1.24.11
6

Quantum groups

Skew-primitive elements

Pointed tensor categories

Chevalley's theorem and Chevalley property

Exercises 1.25.3, 1.29.2, 1.31.7
7

Andruskeiwitsch-Schneider conjecture

Cartier-Kostant theorem

Quasi-bialgebras and quasi-Hopf algebras

Exercises 1.34.9, 1.35.3, 1.36.3
8

Quantum traces

Pivotal categories and dimensions

Spherical categories

Multitensor cateogries

Multifusion rings

Frobenius-Perron theorem

Exercises 1.37.2, 1.27.4, 1.38.3, 1.39.3, 1.42.7
9

Tensor categories

Deligne's tensor product

Finite (multi)tensor categories

Categorical freeness

Exercises 1.45.14, 1.49.2
10

Distinguished invertible object

Integrals in quasi-Hopf algebras

Cartan matrix

Basics of Module categories

Exercises 1.52.9, 2.1.4, 2.1.7, 2.5.3, 2.5.8, 2.6.2, 2.6.7
11

Exact module categories

Algebras in categories

Internal Hom

Exercises 2.8.2, 2.8.4, 2.8.6, 2.8.8, 2.9.7, 2.9.8, 2.9.9, 2.9.11, 2.9.13, 2.9.13, 2.9.15, 2.9.16, 2.9.17, 2.9.20, 2.9.23, 2.9.26, 2.10.3, 2.10.9
12

Main Theorem

Categories of module functors

Dual categories

Exercises 2.11.1, 2.11.4, 2.11.5, 2.12.4, 2.13.1