Noncommutative network models. (11th January 2020)

• Record Type: Journal Article
• Authors: Moeller, Joe
• Is Part Of: Mathematical structures in computer science. Volume 30:Number 1(2020)
• Page Start: 14
• Page End: 32
• Publication Date: 2020-01-11
• Subjects: graph product, -- universal algebra, -- Kneser graph, -- monoidal category, -- network; Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S0960129519000161
• Languages: English
• ISSNs: 0960-1295

Abstract

Abstract: Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between all edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct the free network model on a given monoid, which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete.