Categorical Perspectives on Chemical Reaction Networks

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 $[{\mathbf{A}}_2,\mathbf{V}\mathbf{e}\mathbf{c}\mathbf{t}]$. 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 $[{\mathbf{A}}_2,\mathbf{V}\mathbf{e}\mathbf{c}\mathbf{t}]$ back to CRNs and prove an adjunction with the stoichiometric functor.