LEADER 04666nam 22006615 450 001 996466532003316 005 20200704015627.0 010 $a3-319-95001-0 024 7 $a10.1007/978-3-319-95001-3 035 $a(CKB)4100000006674951 035 $a(DE-He213)978-3-319-95001-3 035 $a(MiAaPQ)EBC6307125 035 $a(PPN)230538150 035 $a(EXLCZ)994100000006674951 100 $a20180919d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOperads of Wiring Diagrams$b[electronic resource] /$fby Donald Yau 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XI, 308 p. 437 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2192 311 $a3-319-95000-2 327 $aIntroduction -- 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. 330 $aWiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads. The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak?s conjecture regarding the quotient-freeness of the relational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images. Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2192 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aDynamics 606 $aErgodic theory 606 $aInformation theory 606 $aNeural networks (Computer science)  606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aInformation and Communication, Circuits$3https://scigraph.springernature.com/ontologies/product-market-codes/M13038 606 $aMathematical Models of Cognitive Processes and Neural Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/M13100 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aInformation theory. 615 0$aNeural networks (Computer science) . 615 14$aCategory Theory, Homological Algebra. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aInformation and Communication, Circuits. 615 24$aMathematical Models of Cognitive Processes and Neural Networks. 676 $a621.31924 700 $aYau$b Donald$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721399 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466532003316 996 $aOperads of wiring diagrams$91539999 997 $aUNISA