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Prove missing link for univalence via new branch of cubical

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Frederik Hanghøj Iversen 2018-05-08 18:01:34 +02:00
parent e5d55c7b2b
commit 32e7290fe9
3 changed files with 6 additions and 7 deletions
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libs/agda-stdlib

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Subproject commit fbd8ba7ea84c4b643fd08797b4031b18a59f561d
Subproject commit 4493cf249a1648be2ad365fe94ece337bfbcb5d9

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libs/cubical

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Subproject commit 5b35333dbbd8fa523e478c1cfe60657321ca38fe
Subproject commit 4e5d43a9c75286b3a8750567d75a930674d7720d

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src/Cat/Category.agda
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@ -137,11 +137,10 @@ record RawCategory (ℓa ℓb : Level) : Set (lsuc (ℓa ⊔ ℓb)) where
Univalent[Contr] : Set _
Univalent[Contr] = ∀ A → isContr (Σ[ X ∈ Object ] A ≊ X)
-- From: Thierry Coquand <Thierry.Coquand@cse.gu.se>
-- Date: Wed, Mar 21, 2018 at 3:12 PM
--
-- This is not so straight-forward so you can assume it
postulate from[Contr] : Univalent[Contr] → Univalent
from[Contr] : Univalent[Contr] → Univalent
from[Contr] = ContrToUniv.lemma _ _
where
open import Cubical.Fiberwise
univalenceFrom≃ : Univalent≃ → Univalent
univalenceFrom≃ = from[Contr] ∘ step