Colored Operads (Graduate Studies in Mathematics) by Donald Yau | (PDF) Free Download

Description

The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality. The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.

User’s Reviews

Editorial Reviews: Review An introductory undergraduate course in abstract algebra is sufficient as a prerequisite for almost all of the material covered in the book. One impressive feature of the book is the emphasis on motivating new concepts as they are introduced and providing numerous graphical illustrations to clarify their geometric significance; there are also numerous exercises collected at the ends of the chapters. The author also provides a list of references to related literature to assist the reader who wishes to continue the study of operads beyond the topics covered in this book. –Murray R. Bremner, Mathematical ReviewsThe book contains much valuable information and detail, which can potentially save a struggling newcomer into operad land many hours of frustration. –Ittay Weiss, MAA ReviewsThis book is a useful introduction to colored operads or symmetric multicategories, to the destination of students as well as researchers interested in these objects. –Loïc Foissy, Zentralblatt Math About the Author Donald Yau, The Ohio State University at Newark, OH, USA.

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