Before revision: We extend the groupoid formalism of coupled cell networks as developed by Golubitsky, Stewart and their collaborators by recasting it in a categorical language .
After revision: We extend the groupoid formalism of coupled cell networks as developed by Golubitsky, Stewart and their collaborators . Our approach uses the tools and --- more importantly ---the stance of category theory. This enables us to put the groupoid formalism in a coordinate-free setting and to extend it from ordinary differential equations to vector fields on manifolds .