Hardcover ISBN:  9781470427238 
Product Code:  GSM/170 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Electronic ISBN:  9781470428716 
Product Code:  GSM/170.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 

Book DetailsGraduate Studies in MathematicsVolume: 170; 2016; 428 ppMSC: Primary 18; 05; 06;
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.ReadershipGraduate students and researchers in mathematics and other sciences where operads and colored operads are used.

Table of Contents

Part 1. Graphs and trees

Chapter 1. Directed graphs

Chapter 2. Extra structures on graphs

Chapter 3. Rooted trees

Chapter 4. Collapsing an internal edge

Chapter 5. Grafting of rooted trees

Chapter 6. Grafting and extra structures

Part 2. Category theory

Chapter 7. Basic category theory

Chapter 8. Symmetric monoidal categories

Chapter 9. Colored symmetric sequences and objects

Part 3. Operads and algebras

Chapter 10. Motivation for colored operads

Chapter 11. Colored operads

Chapter 12. Operads in arity 1

Chapter 13. Algebras over colored operads

Chapter 14. Examples of algebras

Chapter 15. Motivation for partial compositions

Chapter 16. Colored pseudooperads

Part 4. Free colored operads

Chapter 17. Motivation for free colored operads

Chapter 18. General operadic composition

Chapter 19. Free colored nonsymmetric operads

Chapter 20. Free colored operads

Further reading


Additional Material

Reviews

'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 finalyear 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.
Nick Gurski, Jahresbericht der Deutschen MathematikerVereinigung 
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 MathematikerVereinigung 
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.
Loïc 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


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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.
Graduate students and researchers in mathematics and other sciences where operads and colored operads are used.

Part 1. Graphs and trees

Chapter 1. Directed graphs

Chapter 2. Extra structures on graphs

Chapter 3. Rooted trees

Chapter 4. Collapsing an internal edge

Chapter 5. Grafting of rooted trees

Chapter 6. Grafting and extra structures

Part 2. Category theory

Chapter 7. Basic category theory

Chapter 8. Symmetric monoidal categories

Chapter 9. Colored symmetric sequences and objects

Part 3. Operads and algebras

Chapter 10. Motivation for colored operads

Chapter 11. Colored operads

Chapter 12. Operads in arity 1

Chapter 13. Algebras over colored operads

Chapter 14. Examples of algebras

Chapter 15. Motivation for partial compositions

Chapter 16. Colored pseudooperads

Part 4. Free colored operads

Chapter 17. Motivation for free colored operads

Chapter 18. General operadic composition

Chapter 19. Free colored nonsymmetric operads

Chapter 20. Free colored operads

Further reading

'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 finalyear 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.
Nick Gurski, Jahresbericht der Deutschen MathematikerVereinigung 
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 MathematikerVereinigung 
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.
Loïc 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