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 still few
mathematically strict models to represent the characteristics of it
because of its difficulty for interpretation. In order to verify the
validity of this concept, this paper proposes a formal description
of autopoiesis based on the theory of category and
Rosen's
perspective of ``closure under efficient
cause'', provides analytic models of life and social systems, and
discusses the effectiveness of autopoiesis in systems sciences
through implication from the model.