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Feb 20, 2015 at 13:45 comment added Urs Schreiber @goblin, that seems rather close in spirit to type theory ncatlab.org/nlab/show/type theory . In its flavors as homotopy type theory ncatlab.org/nlab/show/homotopy+type+theory this is precisely about groupoids whose morphisms are proofs of equivalences... and higher groupoids whose higher morphisms are proofs of equivalences of proofs of equivalences, and so on.
Feb 13, 2015 at 15:49 history edited Joel David Hamkins CC BY-SA 3.0
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Feb 13, 2015 at 15:45 comment added goblin GONE Interesting. There's definitely a strong connection there.
Feb 13, 2015 at 15:33 history answered Joel David Hamkins CC BY-SA 3.0