Operads of Wiring Diagrams

• Main Author: Yau, Donald (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes in Mathematics, 2192
• Subjects: Category theory (Mathematics).; Homological algebra.; Dynamics.; Ergodic theory.; Information theory.; Neural networks (Computer science) .; Category Theory, Homological Algebra.; Dynamical Systems and Ergodic Theory.; Information and Communication, Circuits.; Mathematical Models of Cognitive Processes and Neural Networks.

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...

Table of Contents:

• Introduction
• Part I Wiring Diagrams
• Wiring Diagrams
• Generators and Relations
• Decomposition of Wiring Diagrams
• Finite Presentation
• Finite Presentation for Algebras over Wiring Diagrams
• Part II Undirected Wiring Diagrams
• Undirected Wiring Diagrams
• Generators and Relations
• Decomposition of Undirected Wiring Diagrams
• Finite Presentation for Undirected Wiring Diagrams
• Algebras of Undirected Wiring Diagrams
• Part III Maps Between Operads of Wiring Diagrams
• A Map from Normal to Undirected Wiring Diagrams
• A Map from Wiring Diagrams to Undirected Wiring Diagrams
• Problems.