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felt the desire to have an entry on the general idea (if any) of synthetic mathematics, cross-linking with the relevant examples-entries.
This has much room for being further expanded, of course.
Since “synthetic homnotopy theory” redirects here, I tried to add some pointers, but just a start:
Discussion of synthetic homotopy theory (typically understood as homotopy type theory):
Ulrik Buchholtz, Sec. 3.1 of Higher Structures in Homotopy Type Theory (arXiv:1807.02177)
Mike Shulman, slides 37 onwards in Homotopical trinitarianism:A perspective on homotopy type theory, 2018 (pdf)
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