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28 March 2024
 
  » arxiv » 1711.0037

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Network Models
John C. Baez ; John Foley ; Joseph Moeller ; Blake S. Pollard ;
Date 31 Oct 2017
AbstractNetworks can be combined in many 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 $mathrm{Cat}$, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.
Source arXiv, 1711.0037
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