Lyapunov functions allow you to certify the stability of a dynamical system without having to solve the related system of differential equations. Control Lyapunov functions and control barrier functions extend this idea to control systems and give a constructive way of creating a controller which exhibits a desired behavior: stability and safety respectively. Recently, there have been many generalizations of CLFs and CBFs made to bring the same idea to more complex scenarios. In this talk I will present a categorical framework for CLFs and CBFs for generalized systems that recovers many useful variants. This framework also enables us to combine and find new variants.