
Colored Operads
Donald Yau(Author)
American Mathematical Society (Publisher)
Will be published approx. on 29. February 2016
Book
Hardback
428 pages
978-1-4704-2723-8 (ISBN)
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.
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.
Reviews / Votes
Colored Operads has a very low barrier to entry, and so would be suitable even for strong undergraduates. Each chapter has exercises at the end, so this book could form the core of a final-year reading course or project...The organizational aspects of this book are exceptional, with a very thorough List of Notations, a Table of Contents that is fine enough to be very usable without being so long as to discourage perusal, a helpful List of Main Facts giving concise versions of all major theorems, and a good Index. The Bibliography is varied, with good references to a wide literature on operads. Yau's monograph offers a very careful introduction to the theory of operads that would complement any library on the subject. It has a calculational flavor that sets it apart from other texts, and this makes it accessible to both graduate and strong undergraduate students...it occupies a very interesting space in the operadic literature." - Nick Gurski, Jahresbericht der Deutschen Mathematiker-Vereinigung"This book is a useful introduction to colored operads or symmetric multicategories, to the destination of students as well as researchers interested in these objects." - Loic Foissy, Zentralblatt Math
"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 Reviews
"The book contains much valuable information and detail, which can potentially save a struggling newcomer into operad land many hours of frustration." - Ittay Weiss, MAA Reviews
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
960 gr
ISBN-13
978-1-4704-2723-8 (9781470427238)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Donald Yau, The Ohio State University at Newark, OH, USA.
Content
Graphs and trees: Directed graphs
Extra structures on graphs
Rooted trees
Collapsing an internal edge
Grafting of rooted trees
Grafting and extra structure
Category theory: Basic category theory
Symmetric monoidal categories
Colored symmetric sequences and objects
Operads and algebras: Motivation for colored operads
Colored operads
Operads in arity 1
Algebras over colored operads
Examples of algebras
Motivation for partial compositions
Colored pseudo-operads
Free colored operads: Motivation for free colored operads
General operadic composition
Free colored non-symmetric operads
Free colored operads
Further reading
Bibliography
List of main facts
Index
Extra structures on graphs
Rooted trees
Collapsing an internal edge
Grafting of rooted trees
Grafting and extra structure
Category theory: Basic category theory
Symmetric monoidal categories
Colored symmetric sequences and objects
Operads and algebras: Motivation for colored operads
Colored operads
Operads in arity 1
Algebras over colored operads
Examples of algebras
Motivation for partial compositions
Colored pseudo-operads
Free colored operads: Motivation for free colored operads
General operadic composition
Free colored non-symmetric operads
Free colored operads
Further reading
Bibliography
List of main facts
Index