Since J. von Neumann physicists stick to categories of Hilbert spaces to modelize quantum phenomena. Categories of modules over a ring might represent an alternative if we add axioms (e.g. the existence of particular limits or co-limits) that would respond to the experimental requirements.
A very general setting for the purpose would be abelian categories. Have there been attempts to make use of them?
References:
https://en.wikipedia.org/wiki/Categories_for_the_Working_Mathematician
https://en.wikipedia.org/wiki/Grothendieck%27s_T%C3%B4hoku_paper
http://www.numdam.org/article/BSMF_1962__90__323_0.pdf
https://www.researchgate.net/project/Homological-algebra
Dear Romeo P.G ,
Thank you for your answer and the reference.
What determines a good choice of R? Experimental constraints? Structure of space?
Best,
TK
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