# Lectures on Algebraic Categorification

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*Volodymyr Mazorchuk*

A publication of the European Mathematical Society

The term “categorification” was introduced by Louis Crane
in 1995 and refers to the process of replacing set-theoretic notions by the
corresponding category-theoretic analogues.

This text mostly concentrates on algebraical aspects of the theory,
presented in the historical perspective, but also contains several topological
applications, in particular, an algebraic (or, more precisely,
representation-theoretical) approach to categorification. It consists of
fifteen sections corresponding to fifteen one-hour lectures given during a
Master Class at Aarhus University, Denmark in October 2010. There are some
exercises collected at the end of the text and a rather extensive list of
references. Video recordings of all (but one) lectures are available from the
Master Class website.

The book provides an introductory overview of the subject rather than a
fully detailed monograph. The emphasis is made on definitions, examples and
formulations of the results. Most proofs are either briefly outlined or
omitted. However, complete proofs can be found by tracking references. It is
assumed that the reader is familiar with the basics of category theory,
representation theory, topology, and Lie algebra.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.