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I'm no expert, so the best I can do is point you to the research community gathering around applied category theory.

* A conference series + workshop: https://www.appliedcategorytheory.org/

* A journal: https://compositionality-journal.org/

Check out some of the people involved in organizing these events. Names I've followed include John Baez, Pawel Sobocinski, and Tai-Danae Bradley (all of whom are amazing educators; check out their work!).

Tai-Danae Bradley wrote a pamphlet on applied category theory which is very approachable: https://arxiv.org/pdf/1809.05923.pdf . Also check out Jules Hedges' thoughts on the importance of compositionality: https://julesh.com/2017/04/22/on-compositionality/ .



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