Since the concept of autopoiesis was proposed as a model of minimal living systems by Maturana and Varela, and applied to social systems by Luhmann, there has been only a few mathematically strict models to represent the characteristics of it because of its difficulty for interpretation. In order to explore the validity of this concept, this paper proposes a more general formal description of autopoiesis based on the theory of category. This paper focuses on the distinction of organizations and structures, and then discusses its implications and problems on formalization of autopoiesis.