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. 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.
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Empty Name
параллельно троллит всех в дискуссиях мэйлинг листа по основаниям математики
In my biased opinion, this is not going well by the grandiose standards I apply to everything.
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Empty Name
https://www.youtube.com/watch?v=2w9Br6gHWdI
he just like me fr fr
(за исключением того что он умный а я нет)
(за исключением того что он умный а я нет)
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Empty Name
https://www.youtube.com/watch?v=2w9Br6gHWdI
в принципе играет он настолько же странно как я
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Empty Name
BACK TO THE ROOTS (мое понимание HoTT находится на уровне 90х годов)
удивительно что люди писали статьи в 1996 году.
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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.
But I will.
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-Dude, I love you. I don’t know the fuck who you are. But… you’re crazy. I am inspired by you. 1AM and you’re still studying… like wtf
-Thanks, I guess. How many drinks have you had?
-Thanks, I guess. How many drinks have you had?
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Empty Name
-Dude, I love you. I don’t know the fuck who you are. But… you’re crazy. I am inspired by you. 1AM and you’re still studying… like wtf -Thanks, I guess. How many drinks have you had?
little did he know что днем я пинаю хуй, а работаю ночью
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