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Jan 19, 2022 at 3:49 comment added user41282141 As phrased, the Wikipedia claim is somewhat suspect. What the section on Morse theory is hinting at is that derived geometry provides a conceptual explanation of certain "enhancements" of spaces that appear as critical loci. So derived geometry is related to things like virtual fundamental classes and Floer homology. (You don't really need derived geometry these, but it provides a nice framework).
Jan 19, 2022 at 0:37 comment added Jason Starr You might also look at Kapranov-Vasserot.
Jan 19, 2022 at 0:00 history asked user127776 CC BY-SA 4.0