This note covers the following
topics: Monoidal categories, The pentagon axiom, Basic properties of unit
objects in monoidal categories, monoidal categories, Monoidal functors,
equivalence of monoidal categories, Morphisms of monoidal functors, MacLane's
strictness theorem, The MacLane coherence theorem, Invertible objects,
Exactness of the tensor product, Semisimplicity of the unit object, Groupoids,
Finite abelian categories and exact faithful functors, Fiber functors, Hopf
algebras, Pointed tensor categories and pointed Hopf algebras, Chevalley's
theorem, The Andruskiewitsch-Schneider conjecture, The Cartier-Kostant
theorem, Pivotal categories and dimensions, Spherical categories and
Grothendieck rings of semisimple tensor categories.

**Author(s):** P.
Etingof, S. Gelaki, D. Nikshych, and V. Ostrik

393**Pages**