What is a thought process? categorical sheaf-theoretic approach

Abstract

Categorical formulations for thought processes and communications are provided. In order to treat the changing state of an individual over some time period, we introduce a state controlling “variable” in terms of objects (called generalized time) in a site (i.e., a category with a Grothendieck topology). We also capture communications (information flows) as observation morphisms between individuals. The interplay among the change of the state of an individual, the communication between individuals, and thought processes of those individuals is unified as the commutativities of the fundamental diagram in section 3. Finally, we show that the thought process (thinking) coincides with “thinking nothing” (process) when the thought process morphism coincides with the induced morphism from the identity.