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To properly talk about compositionality in differential equations you absolutely need category theory. Likewise I firmly believe that PDE and numerical mathemat
by orbifold 4y ago
To properly talk about compositionality in differential equations you absolutely need category theory. Likewise I firmly believe that PDE and numerical mathematics actually lack a good foundation in category theory, not that they don’t need one.
It is just very hard to create non-trivial general theories in sich „Applied“ fields, Functional Analysis alone is not very exciting. For an example see for example the work or Hairer (stochastic differential equations) or Costello (QFT).
- hackandthink 4y agoGrothendieck stacks in QFT, did not know about it. This is wild stuff: https://people.math.umass.edu/~mirkovic/0.SEMINARS/1.QFT/C.Costello/Perturbative.QFT.pdf https://people.math.umass.edu/~mirkovic/0.SEMINARS/1.QFT/C.C... funny names: a Leonard Cohen writing about an Costello (but Kevin Costello not Elvis Costello)