Operads of Wiring Diagrams

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Operads of Wiring Diagrams by Donald Yau, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Donald Yau ISBN: 9783319950013
Publisher: Springer International Publishing Publication: September 19, 2018
Imprint: Springer Language: English
Author: Donald Yau
ISBN: 9783319950013
Publisher: Springer International Publishing
Publication: September 19, 2018
Imprint: Springer
Language: English

Wiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads.

The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak’s conjecture regarding the quotient-freeness of the relational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images.

Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Wiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads.

The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak’s conjecture regarding the quotient-freeness of the relational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images.

Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study.

More books from Springer International Publishing

Cover of the book The Coming Crisis by Donald Yau
Cover of the book Decision and Game Theory for Security by Donald Yau
Cover of the book The International Court of Justice by Donald Yau
Cover of the book Academic Theories of Generation in the Renaissance by Donald Yau
Cover of the book Handbook of Maleic Anhydride Based Materials by Donald Yau
Cover of the book Brain-Machine Interface by Donald Yau
Cover of the book Cecil B. DeMille, Classical Hollywood, and Modern American Mass Culture by Donald Yau
Cover of the book ICT Systems Security and Privacy Protection by Donald Yau
Cover of the book Information Literacy in Everyday Life by Donald Yau
Cover of the book Murdoch on Truth and Love by Donald Yau
Cover of the book Political and Legal Perspectives of the EU Eastern Partnership Policy by Donald Yau
Cover of the book Learning and Teaching Real World Problem Solving in School Mathematics by Donald Yau
Cover of the book Mathematics Matters in Education by Donald Yau
Cover of the book IR Theory, Historical Analogy, and Major Power War by Donald Yau
Cover of the book Advances in Affective and Pleasurable Design by Donald Yau
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy