By Volodymyr Mazorchuk
The time period "categorification" was once brought by means of Louis Crane in 1995 and refers back to the means of exchanging set-theoretic notions via the corresponding category-theoretic analogues. this article regularly concentrates on algebraical points of the idea, provided within the ancient viewpoint, but additionally includes a number of topological purposes, specifically, an algebraic (or, extra accurately, representation-theoretical) method of categorification. It contains fifteen sections resembling fifteen one-hour lectures given in the course of a grasp classification at Aarhus collage, Denmark in October 2010. There are a few workouts amassed on the finish of the textual content and a slightly large checklist of references. Video recordings of all (but one) lectures can be found from the grasp category web site. The publication offers an introductory evaluate of the topic instead of an absolutely unique monograph. The emphasis is made on definitions, examples and formulations of the implications. such a lot proofs are both in short defined or passed over. even if, whole proofs are available by way of monitoring references. it really is assumed that the reader is aware the fundamentals of classification conception, illustration thought, topology, and Lie algebra. A book of the ecu Mathematical Society (EMS). dispensed in the Americas via the yankee Mathematical Society.
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