Use explicit parameter for hSet

This commit is contained in:
Frederik Hanghøj Iversen 2018-03-21 15:01:31 +01:00
parent ae0ff092f8
commit 8f67ff9f36
2 changed files with 16 additions and 7 deletions

View file

@ -59,10 +59,8 @@ module _ { : Level} {A B : Set } {a : A} where
module _ ( : Level) where
private
open import Cubical.Universe using (hSet) public
SetsRaw : RawCategory (lsuc )
RawCategory.Object SetsRaw = hSet {}
RawCategory.Object SetsRaw = hSet
RawCategory.Arrow SetsRaw (T , _) (U , _) = T U
RawCategory.𝟙 SetsRaw = Function.id
RawCategory._∘_ SetsRaw = Function._∘_
@ -79,7 +77,7 @@ module _ ( : Level) where
arrowsAreSets {B = (_ , s)} = setPi λ _ s
isIso = Eqv.Isomorphism
module _ {hA hB : hSet {}} where
module _ {hA hB : hSet } where
open Σ hA renaming (proj₁ to A ; proj₂ to sA)
open Σ hB renaming (proj₁ to B ; proj₂ to sB)
lem1 : (f : A B) isSet A isSet B isProp (isIso f)
@ -284,7 +282,7 @@ module _ ( : Level) where
univalent' : hA isContr (Σ[ hB Object ] hA hB)
univalent' hA = {!!} , {!!}
module _ {hA hB : hSet {}} where
module _ {hA hB : hSet } where
-- Thierry: `thr0` implies univalence.
univalent : isEquiv (hA hB) (hA hB) (Univalence.id-to-iso (λ {A} {B} isIdentity {A} {B}) hA hB)

View file

@ -17,7 +17,7 @@ open import Cubical.GradLemma
using (gradLemma)
public
open import Cubical.NType
using (⟨-2⟩)
using (⟨-2⟩ ; ⟨-1⟩ ; ⟨0⟩ ; TLevel ; HasLevel)
public
open import Cubical.NType.Properties
using
@ -25,7 +25,18 @@ open import Cubical.NType.Properties
; propPi ; propHasLevel ; setPi ; propSet)
public
open import Cubical.Sigma using (setSig ; sigPresSet) public
open import Cubical.Universe using (hSet) public
module _ ( : Level) where
-- FIXME Ask if we can push upstream.
-- A redefinition of `Cubical.Universe` with an explicit parameter
_-type : TLevel Set (lsuc )
n -type = Σ (Set ) (HasLevel n)
hSet : Set (lsuc )
hSet = ⟨0⟩ -type
Prop : Set (lsuc )
Prop = ⟨-1⟩ -type
-----------------
-- * Utilities --