In algebraic topology, there are a lot of commutative diagrams and commutative diagrams up to homotopy. Different ways of compositions of maps in a commutative diagram are equal or homotopy equivalent.

An example of commutative diagrams in algebraic topology

In organic synthesis, there are some diagrams consisting of synthetic routes. Different ways of chemical reactions produces the same product.

An example of diagrams of synthetic routes

Question: are there any really useful research topics about the application of commutative diagrams in mathematics into organic synthesis?

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    $\begingroup$ I would say that chemical reactions are more similar to network flows (graph theory, operations research) than to commutative diagrams. Commutative diagrams express a notion that we will get the same result regardless of the path taken through a necessarily "boxy" diagram, while in organic synthesis the yields going through one path may differ significantly from the yields going another path. So even if somehow one can afford to ignore multiple species (reactants) in an organic synthesis, restricting ourselves to commutative diagrams sacrifices an important quantitative goal. $\endgroup$ – hardmath Mar 13 '16 at 11:10

John Baez's has recently worked on something related: he modeled Petri nets and chemical reaction inside the framework of category theory. His work can be found on this link.

Hope this address your question.


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