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Venue
Foundational
Methods in Computer Science 2006,
Kananaskis Field Station (University of Calgary),
7/6/06
Abstract This is an introduction to the theory and applications of operads, with the emphasis on the theory. In the first half I will give the basic definitions. Operads can be viewed in two ways: (i) as algebraic theories; (ii) as categorical structures in their own right. (Compare Lawvere theories.) I will explain the two viewpoints and how they can be useful in some diverse mathematical situations. In the second half I will describe some generalizations of the notion of operad useful in higher category theory. Again, such generalized operads can be viewed in two ways: (i) as algebraic theories of a rather sophisticated kind (including, for instance, various theories of n-categories); (ii) as higher categorical structures in their own right, of independent interest. Slides In this pdf file (4.4MB). More detail on most of the topics can be found in my book.
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