First Steps towards Categorical Algebraic Artificial Chemistry

TL;DR

This paper introduces a categorical framework for modeling the dynamics of algebraic artificial chemistry, generalizing existing computational models and proposing future directions for formalizing chemical interactions using category theory.

Contribution

It develops a functorial approach to assign dynamics to algebraic models of interacting components, extending the AlChemy model with categorical methods.

Findings

Constructed a functor for dynamics in algebraic models

Generalized the AlChemy model using category theory

Outlined future research directions in formalizing chemical interactions

Abstract

We construct a functor that gives a dynamics to an algebraic model of interacting components. The construction generalises a computational model of Fontana and Buss in the field of artificial life known as AlChemy, in which molecules and their chemical interactions are emulated by lambda calculus terms and their application and subsequent reduction. We discuss future directions for the application of category theory to algebraic artificial chemistry as an organisational tool, with a focus on formalising the connection between the algebraic and the dynamical facets of such models.