Colored Operads

Donald Yau, The Ohio State University at Newark, OH, USA.

• Graphs and trees: Directed graphsExtra structures on graphsRooted treesCollapsing an internal edgeGrafting of rooted treesGrafting and extra structureCategory theory: Basic category theorySymmetric monoidal categoriesColored symmetric sequences and objectsOperads and algebras: Motivation for colored operadsColored operadsOperads in arity 1Algebras over colored operadsExamples of algebrasMotivation for partial compositionsColored pseudo-operadsFree colored operads: Motivation for free colored operadsGeneral operadic compositionFree colored non-symmetric operadsFree colored operadsFurther readingBibliographyList of main factsIndex

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." - 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