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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)
I noticed that the link “synthetic homotopy theory” didn’t go anywhere. Have made it a redirect to synthetic mathematics now, since that is the entry which has a subsection “Synthetic homotopy theory”. Optimally it should be given it’s own entry, though.
Sorry that was me. I was in the process of setting up a new page yesterday, but removing the redirect didn’t generate the usual ? link, and I got called away. I’ll see if I have time today.
Oh, I see. All the better! Let’s create that page, when anyone finds the time.
I’m trying again, have removed the redirect, but synthetic homotopy theory still ends up at synthetic mathematics
Redirected from “synthetic homotopy theory”
Removed now. Think there is a little bug in such cases, which submitting an edit after the first one usually solves. I’ll try to fix the bug when I get a chance.
Thanks!
Just to clarify that the “recently active area” mentioned in #11 is probably the “synthetic Tait computatibility theory” (now requested here)
Just to be clear, “synthetic Tait computatibility” is not a subfield of “synthetic computability theory”
Would be good to further expand on this at synthetic Tait computability, because this is surprising, given the terminology: I gather then it must be true that also “Tait computability” is not a subfield of “computability”?!
I’ll try to write something about it soon… It is indeed separate from computability theory; the history is that there is a central technique in CS/Logic called “Tait’s Method of Computability” that I abstracted synthetically. It corresponds to working synthetically in a glued topos, i.e. a topos equipped with a distinguished subterminal.
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