What would a monoidal closed structure mean for the resource theory of chemistry?
For any two material collections, one can form a material collection \(c \multimap d\) with the property that, for any a one has \(a + c \rightarrow d\) iff \(a \rightarrow (c \multimap d)\)
Concretely, say we have \(2 H_2O + 2 Na \rightarrow 2 NaOH + H_2\), we must also have \(2H_2O \rightarrow (2Na \multimap (2NaOH+H_2))\)
From two molecules of water, you can form a certain substance. This doesn’t make sense, so maybe this symmetric monoidal preorder is not closed.
Alternatively, think of the substance \(2Na \multimap (2NaOH+H_2)\) as a potential reaction, that of converting sodium to sodium-hyroxide+hydrogen. Two molecules of water unlock that potential. NOCARD