By Volodymyr Mazorchuk
The time period “categorification” used to be brought by way of Louis Crane in 1995 and refers back to the technique of exchanging set-theoretic notions by means of the corresponding category-theoretic analogues.
This textual content ordinarily concentrates on algebraical elements of the idea, awarded within the old viewpoint, but in addition includes numerous topological functions, particularly, an algebraic (or, extra accurately, representation-theoretical) method of categorification. It includes fifteen sections reminiscent of fifteen one-hour lectures given in the course of a grasp classification at Aarhus college, Denmark in October 2010. There are a few workouts amassed on the finish of the textual content and a slightly wide record of references. Video recordings of all (but one) lectures can be found from the grasp category website.
The ebook offers an introductory evaluate of the topic instead of a completely distinct monograph. Emphasis is on definitions, examples and formulations of the consequences. so much proofs are both in brief defined or passed over. although, entire proofs are available by means of monitoring references. it really is assumed that the reader is aware the fundamentals of type thought, illustration idea, topology and Lie algebra.