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John Baez (May 06 2026 at 12:02):Mauricio Montes emailed me about this paper:
It defines a new category of reaction networks where the rate constants are not part of the data of a reaction network, since they don't want to assume the law of mass action as the rule for determining the rates of reactions. So you can't get a specific set of differential equations from one of their reaction networks, but the morphisms are more flexible. This allows them to talk about "reduction morphisms" which simplify a reaction network. They say an earlier attempt to do this, by Yuji Hirono, Takashi Okada, Hiroyasu Miyazaki, and Yoshimasa Hidaka, didn't work correctly.
They also define and study zeroth and first homology groups of a reaction network, which seem to match what I'd expect.
I should probably do another round of thinking about reaction networks, based on this paper!