Networks can be combined in various ways, such as overlaying one on top of
another or setting two side by side. We introduce "network models" to encode
these ways of combining networks. Different network models describe different
kinds of networks. We show that each network model gives rise to an operad,
whose operations are ways of assembling a network of the given kind from
smaller parts. Such operads, and their algebras, can serve as tools for
designing networks. Technically, a network model is a lax symmetric monoidal
functor from the free symmetric monoidal category on some set to
Cat, and the construction of the corresponding operad proceeds via a
symmetric monoidal version of the Grothendieck construction.Comment: 46 page
