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Operads of Wiring Diagrams (Paperback, 1st ed. 2018)
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Operads of Wiring Diagrams (Paperback, 1st ed. 2018)
Series: Lecture Notes in Mathematics, 2192
Expected to ship within 10 - 15 working days
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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.
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