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 [A2,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 [A2,Vect] back to CRNs and prove an adjunction with the stoichiometric functor.
@article{arxiv.2604.04919,
title = {Categorical Perspectives on Chemical Reaction Networks},
author = {Justin Curry and Mauricio Montes},
journal= {arXiv preprint arXiv:2604.04919},
year = {2026}
}