Determination through Universals: An Application of Category Theory in the Life Sciences

TL;DR

This paper applies category theory, specifically semiadjunctions, to model universal determination processes in the life sciences, offering a new conceptual framework for understanding biological and cognitive phenomena.

Contribution

It reformulates adjunctions using heteromorphisms, introducing semiadjunctions as a novel tool for modeling universal determination in empirical sciences.

Findings

Semiadjunctions characterize three principal schemes of determination.

Application to biological and cognitive processes such as natural selection and language.

Provides a new categorical framework for life sciences phenomena.

Abstract

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics---with adjunctions being the primary lense. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction (or half-adjunuction). Semiadjunctions (essentially a formulation of a universal mapping property using hets) turn out to be the appropriate concept for applications in the life sciences. The semiadjunctions characterize three principal schemes with applications: 1. determination through a receiving universal (e.g., natural selection, perception, language acquisition, recursion, and language understanding); 2. determination through a sending universal (e.g., intentional action, DNA mechanism to build amino acids, hierarchy of regulatory genes to build organs, stem cells, and language production), and 3. two-way determination with one universal as both receiving and sending (e.g., perception/action and language understanding/production).