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The purpose of this paper is to define a bunch of operads where the operations are networks of a certain type. The way we specify what type of network we want is with something we call a network model. This is basically a combinatorial species which has extra structure capturing the notions of union and disjoint union. The corresponding operad is then constructed via a moniodal variant of the Grothendieck construction.
Martin Markl?, Steve Shnider?, James D. Stasheff?, Operads in algebra, topology and physics?, Math. Surveys and Monographs 96, Amer. Math. Soc. 2002.
F. Bergeron?, G. Labelle?, and P. Leroux?, Combinatorial Species and Treelike Structures?, Cambridge, Cambridge U. Press, 1998.
B. Day? and R. Street?, Monoidal bicategories and Hopf algebroids, Adv. Math. 129, pages 99–157, 1997.
A. Joyal?, Une théorie combinatoire des séries formelles, Advances in Mathematics 42, pages 1-82, 1981.