Colored Operads
Seiten
2016
American Mathematical Society (Verlag)
978-1-4704-2723-8 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2723-8 (ISBN)
Explores the theory of operads and coloured operads, sometimes called symmetric multicategories. A (coloured) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. Topics covered include basic graph theory, basic category theory, colored operads, and algebras over coloured operads.
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 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.
Donald Yau, The Ohio State University at Newark, OH, USA.
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
| Erscheinungsdatum | 25.03.2016 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 960 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-2723-0 / 1470427230 |
| ISBN-13 | 978-1-4704-2723-8 / 9781470427238 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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