Abstract
In this chapter we first recall two equivalent definitions of a colored operad. Then we recall wiring diagrams whose wires carry values in an arbitrary class and prove that they form an operad.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Awodey, Category Theory, 2nd. ed., Oxford Logic Guides 52, Oxford Univ. Press, Oxford, 2010.
P.R. Halmos, Naive Set Theory, Undergrad. Texts in Math., Springer, New York, 1974.
M.W. Johnson and D. Yau, On homotopy invariance for algebras over colored PROPs, J. Homotopy and Related Structures 4 (2009), 275–315.
G.M. Kelly, On the operads of J.P. May, Reprints in Theory Appl. Categ. 13 (2005), 1–13.
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.
T. Leinster, Basic Category Theory, Cambridge Studies in Adv. Math. 143, Cambridge Univ. Press, Cambridge, 2014.
S. Mac Lane, Categories for the working mathematician, Grad. Texts in Math. 5, 2nd ed., Springer-Verlag, New York, 1998.
C. Male, Traffics distributions and independence: the permutation invariant matrices and the notions of independence, arXiv:1114.4662v6.
M. Markl, Models for operads, Comm. Algebra 24 (1996), 1471–1500.
M. Markl, Operads and PROPs, Handbook of Algebra 5, p. 87–140, Elsevier, 2008.
M. Markl, S. Shnider, and J. Stasheff, Operads in Algebra, Topology and Physics, Math. Surveys and Monographs 96, Amer. Math. Soc., Providence, 2002.
J.P. May, Definitions: operads, algebras and modules, Contemp. Math. 202, p. 1–7, 1997.
C.C. Pinter, A Book of Set Theory, Dover, New York, 2014.
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 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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Yau, D. (2018). Wiring Diagrams. In: Operads of Wiring Diagrams. Lecture Notes in Mathematics, vol 2192. Springer, Cham. https://doi.org/10.1007/978-3-319-95001-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-95001-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95000-6
Online ISBN: 978-3-319-95001-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)