Finite Automata Networks (FANs) and Finite Binary Functions (FBFs) are two kinds of finite dynamical systems. In this paper FAN morphisms and FBF morphisms are introduced. The limit structures of the resulting categories {\bf FAN} and {\bf FBF} are studied. It is shown that they are both finitely complete. Finally, a well-known adjunction from directed graphs into sets is lifted to the finite dynamical system level to obtain an adjunction between {\bf FAN} and {\bf FBF}.