Dynamical systems with an underlying network structure are a subject of great interest as they arise frequently in applications and exhibit many staggering phenomena some of which resemble those in equivariant dynamics. We introduce a theory developed by Rink and Sanders that connects a class of network dynamical systems - namely homogeneous coupled cell systems - to equivariant dynamical systems. The symmetries, however, are generalized in the sense that they do not necessarily form a group but more general structures such as monoids or semigroups. We investigate how to exploit these symmetries in order to understand the generic bifurcation behavior of a given network. Finally we present some ideas and open questions on how to exploit representation theory of finite monoids in order to further deepen the understanding of networks.