Categorical Perspectives on Chemical Reaction Networks

TL;DR

This paper explores the categorical structure underlying chemical reaction network reductions, revealing functorial properties and universal constructions that deepen the theoretical understanding of CRN simplifications.

Contribution

It establishes the categorical interpretation of CRN reductions, introduces a reconstruction functor, and proves an adjunction with the stoichiometric functor.

Findings

Identifies the categorical complement of the stoichiometric arrow as the Schur-complement reduction.

Shows the ambient category for topological reduction is functorial.

Defines a reconstruction functor and proves an adjunction with the stoichiometric functor.

Abstract

We show that the Schur-complement reduction of a chemical reaction network (CRN) from Hirono et al. is the categorical complement of the stoichiometric arrow in the arrow category $[\mathbf{A}_2,\mathbf{Vect}]$. This identifies the ambient category in which topological reduction of chemical reaction networks is functorial and explains the reduced stoichiometric matrix as a universal diagrammatic construction. We further define a reconstruction functor from a restricted subcategory of $[\mathbf{A}_2, \mathbf{Vect}]$ back to CRNs and prove an adjunction with the stoichiometric functor.