Abstract
In this introductory chapter, we provide a brief overview of wiring diagrams. Then we describe the purposes of this monograph and the content of each subsequent chapter.
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References
M.F. Atiyah and I.G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Massachusetts, 1969.
J.C. Baez and J. Erbele, Categories in control, Theory Appl. Categ. 30 (2015), 836–881.
F. Bonchi, P. Sobociński, and F. Zanasi, A categorical semantics of signal flow graphs, pp. 435–450, Lecture Notes in Comp. Sci. 8704, Springer, 2014.
V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994), 203–272.
A. Joyal, R. Street, and D. Verity, Traced monoidal categories, Mathematical Proceedings of the Cambridge Philosophical Society 119 (1996), 447–468.
J. Lambek, Deductive systems and categories. II. Standard constructions and closed categories, in: 1969 Category Theory, Homology Theory and their Applications, I (Battelle Inst. Conf., Seattle, Wash., 1968, Vol. 1) p. 76–122, Springer, Berlin, 1969.
S. Mac Lane, Natural Associativity and Commutativity, Rice Univ. Studies 49, No. 4 (1963), 28–46.
S. Mac Lane, Categories for the working mathematician, Grad. Texts in Math. 5, 2nd ed., Springer-Verlag, New York, 1998.
J.P. May, The geometry of iterated loop spaces, Lecture Notes in Math. 271, Springer-Verlag, New York, 1972.
J.P. May, Definitions: operads, algebras and modules, Contemp. Math. 202, p. 1–7, 1997.
J.J. Rotman, Advanced Modern Algebra, Prentice Hall, New Jersey, 2002.
D. Rupel and D.I. Spivak, The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes, arXiv:1307.6894.
D.I. Spivak, The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits, arXiv:1305.0297.
D.I. Spivak, Category Theory for the Sciences, MIT Press, 2014.
D.I. Spivak, The steady states of coupled dynamical systems compose according to matrix arithmetic, arXiv:1512.00802.
D.I. Spivak, P. Schultz, and D. Rupel, String diagrams for traced and compact categories are oriented 1-cobordisms, arXiv:1508.01069.
D.I. Spivak and J.Z. Tan, Nesting of dynamic systems and mode-dependent networks, arXiv:1502.07380.
D. Vagner, D.I. Spivak, and E. Lerman, Algebras of open dynamical systems on the operad of wiring diagrams, Theory Appl. Categ. 30 (2015), 1793–1822.
D. Yau, Colored Operads, Graduate Studies in Math. 170, Amer. Math. Soc., Providence, RI, 2016.
D. Yau and M.W. Johnson, A Foundation for PROPs, Algebras, and Modules, Math. Surveys and Monographs 203, Amer. Math. Soc., Providence, RI, 2015.
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Yau, D. (2018). Introduction. In: Operads of Wiring Diagrams. Lecture Notes in Mathematics, vol 2192. Springer, Cham. https://doi.org/10.1007/978-3-319-95001-3_1
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DOI: https://doi.org/10.1007/978-3-319-95001-3_1
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