The Resource Operads of Wiring Diagrams, by Donald Yau, (electronic resource)

Operads of Wiring Diagrams, by Donald Yau, (electronic resource)

Label
Operads of Wiring Diagrams
Title
Operads of Wiring Diagrams
Statement of responsibility
by Donald Yau
Creator
Author
Author
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Yau, Donald
Dewey number
512.6
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
GC0MCC6hWjk
Image bit depth
0
LC call number
QA169
Literary form
non fiction
Series statement
Lecture Notes in Mathematics,
Series volume
2192
http://library.link/vocab/subjectName
  • Algebra
  • Differentiable dynamical systems
  • Mathematics
  • Category Theory, Homological Algebra
  • Dynamical Systems and Ergodic Theory
  • Information and Communication, Circuits
  • Mathematical Models of Cognitive Processes and Neural Networks
Label
Operads of Wiring Diagrams, by Donald Yau, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource (XI, 308 p. 437 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783319950013
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-95001-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4100000006674951
  • (DE-He213)978-3-319-95001-3
  • (EXLCZ)994100000006674951
Label
Operads of Wiring Diagrams, by Donald Yau, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource (XI, 308 p. 437 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783319950013
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-95001-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4100000006674951
  • (DE-He213)978-3-319-95001-3
  • (EXLCZ)994100000006674951

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