Use explicit parameter for hSet
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@ -59,10 +59,8 @@ module _ {ℓ : Level} {A B : Set ℓ} {a : A} where
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module _ (ℓ : Level) where
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private
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open import Cubical.Universe using (hSet) public
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SetsRaw : RawCategory (lsuc ℓ) ℓ
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RawCategory.Object SetsRaw = hSet {ℓ}
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RawCategory.Object SetsRaw = hSet ℓ
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RawCategory.Arrow SetsRaw (T , _) (U , _) = T → U
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RawCategory.𝟙 SetsRaw = Function.id
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RawCategory._∘_ SetsRaw = Function._∘′_
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@ -79,7 +77,7 @@ module _ (ℓ : Level) where
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arrowsAreSets {B = (_ , s)} = setPi λ _ → s
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isIso = Eqv.Isomorphism
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module _ {hA hB : hSet {ℓ}} where
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module _ {hA hB : hSet ℓ} where
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open Σ hA renaming (proj₁ to A ; proj₂ to sA)
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open Σ hB renaming (proj₁ to B ; proj₂ to sB)
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lem1 : (f : A → B) → isSet A → isSet B → isProp (isIso f)
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@ -284,7 +282,7 @@ module _ (ℓ : Level) where
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univalent' : ∀ hA → isContr (Σ[ hB ∈ Object ] hA ≅ hB)
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univalent' hA = {!!} , {!!}
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module _ {hA hB : hSet {ℓ}} where
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module _ {hA hB : hSet ℓ} where
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-- Thierry: `thr0` implies univalence.
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univalent : isEquiv (hA ≡ hB) (hA ≅ hB) (Univalence.id-to-iso (λ {A} {B} → isIdentity {A} {B}) hA hB)
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@ -17,7 +17,7 @@ open import Cubical.GradLemma
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using (gradLemma)
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public
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open import Cubical.NType
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using (⟨-2⟩)
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using (⟨-2⟩ ; ⟨-1⟩ ; ⟨0⟩ ; TLevel ; HasLevel)
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public
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open import Cubical.NType.Properties
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using
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@ -25,7 +25,18 @@ open import Cubical.NType.Properties
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; propPi ; propHasLevel ; setPi ; propSet)
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public
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open import Cubical.Sigma using (setSig ; sigPresSet) public
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open import Cubical.Universe using (hSet) public
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module _ (ℓ : Level) where
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-- FIXME Ask if we can push upstream.
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-- A redefinition of `Cubical.Universe` with an explicit parameter
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_-type : TLevel → Set (lsuc ℓ)
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n -type = Σ (Set ℓ) (HasLevel n)
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hSet : Set (lsuc ℓ)
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hSet = ⟨0⟩ -type
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Prop : Set (lsuc ℓ)
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Prop = ⟨-1⟩ -type
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-----------------
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-- * Utilities --
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