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Friday, September 4, 2015

**Abstract:** Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalize these kinds of structures as algebras over presentable colored operads. DeVille and Lerman, building on the groupoid formalism for coupled cell networks of Golubitsky, Stewart and collaborators, proposed an approach to the study of dynamics of complex systems which is based on graph fibrations. My goal is to describe an algebraic framework that encompasses both the operadic approache of Spivak et al. and fibrations of networks of manifolds of DeVille and Lerman.