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Немає даних24 години
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-Dude, I love you. I don’t the fuck who you are. But… you’re crazy. I am inspired by you.
-Thanks, I guess. How many drinks have you had?
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> Whatever you like. I’m not about to spend time arguing about language at that meta of a level!
But I will.
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In my biased opinion, this is not going well by the grandiose standards I apply to everything.
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Зафиксирую: HoTT is intensional even though it usually takes FunExt as an axiom or as a theorem, since it doesn't have UIP. UIP holds in set-theoretic models aka "types as sets" of ITT/HoTT, but not in simplicial/cubical-sets models (aka types are indeed 8-grpds, where every model deals with higher paths in its own fashion). In MLTT identity types are inductive type families (thus intensionality and 8-grpd structure) and UA allows to calculфte path spaces of higher inductives. Even though UA implies FunExt. ERR implies UIP since it allows to get definitional equality from an inhabitant of identity type (aka there is a witness of equality between term p of identity type Id_A(a,b) and refl(a)) . In homotopical interpretation UIP trivilizes higher paths ---> UIP + FunExt = extensionality and ERR also implies FunExt. Done.
