[4S1-OS-30a] OS-30

[4S1-OS-30a-05] Self as a Monoid: A Category-Theoretic Approach to Autonomy

〇Ryuzo Hirota¹, Hayato Saigo², Shigeru Taguchi³ (1. University of Tokyo, 2. Nagahama Institute of Bio-Science and Technology, 3. Hokkaido University)

Keywords:Autonomy, Category Theory, Monoid, Self, Closure

Life maintains its individuality while continuously changing its components and state through interaction with the external world. This property, referred to as "autonomy," distinguishes life from non-life and has been the subject of various formalization attempts. Notably, the concept of "closure," denoting the property of returning to its original state or domain through specific operations or processes, has played a pivotal role. Here, to provide a more concise understanding of the essential nature of autonomy, we introduce our proposal of the formalization of autonomy as a "monoid" (a category with only one object), the simplest mathematical formalization of "closure" in general.
According to our proposal, autonomy can be understood as a monoid of "mediation," in which the "self" mediates itself. This general formalization of autonomy would lead to a deeper comprehension not only of biological autonomy but also of the broader phenomenon known as "self."