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2 changes: 1 addition & 1 deletion Cubical/Algebra/Algebra/Properties.agda
Original file line number Diff line number Diff line change
Expand Up @@ -110,7 +110,7 @@ module AlgebraEquivs where
(invAlgebraEquiv {A = A} {B = B} f').snd = hom
where
open AlgebraStr {{...}}
private instance
instance
_ = snd A
_ = snd B

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10 changes: 4 additions & 6 deletions Cubical/Algebra/CommRing/Localisation/UniversalProperty.agda
Original file line number Diff line number Diff line change
Expand Up @@ -373,12 +373,10 @@ module _ (R' : CommRing ℓ) (S' : ℙ (fst R')) (SMultClosedSubset : isMultClos
; ·IdR to ·A-rid)
open Units A' renaming (Rˣ to Aˣ ; RˣInvClosed to AˣInvClosed)
open PathToS⁻¹R ⦃...⦄
private
A = fst A'
instance
_ = cond
χ = (S⁻¹RHasUniversalProp A' φ φS⊆Aˣ .fst .fst)
open RingHomTheory χ
A = fst A'
instance _ = cond
χ = (S⁻¹RHasUniversalProp A' φ φS⊆Aˣ .fst .fst)
open RingHomTheory χ

S⁻¹R≃A : S⁻¹R ≃ A
S⁻¹R≃A = fst χ , isEmbedding×isSurjection→isEquiv (Embχ , Surχ)
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3 changes: 1 addition & 2 deletions Cubical/AlgebraicGeometry/ZariskiLattice/StructureSheaf.agda
Original file line number Diff line number Diff line change
Expand Up @@ -137,8 +137,7 @@ module _ {ℓ : Level} (R' : CommRing ℓ) where
open S⁻¹RUniversalProp R' [ f ⁿ|n≥0] (powersFormMultClosedSubset f) using (_/1)
open RadicalIdeal R'

private
instance
instance
_ = snd R[1/ f ]AsCommRing

f∈√⟨g⟩ : f ∈ √ ⟨ g ⟩ₛ
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Original file line number Diff line number Diff line change
Expand Up @@ -158,8 +158,7 @@ module _ (R' : CommRing ℓ) where
open S⁻¹RUniversalProp R' [ f ⁿ|n≥0] (powersFormMultClosedSubset f) using (_/1)
open RadicalIdeal R'

private
instance
instance
_ = snd R[1/ f ]AsCommRing

Df≤Dg : D f ≤ D g
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9 changes: 4 additions & 5 deletions Cubical/Categories/DistLatticeSheaf/Extension.agda
Original file line number Diff line number Diff line change
Expand Up @@ -736,11 +736,10 @@ module PreSheafExtension (L : DistLattice ℓ) (C : Category ℓ' ℓ'')
s₁ (cospanPath i) = DLRan F .F-hom (≤m→≤j _ _ (∧≤LCancel _ _))
s₂ (cospanPath i) = DLRan F .F-hom (≤m→≤j _ _ (∧≤RCancel _ _))

private
F[⋁β]Cone = limitC _ (F* (⋁ β)) .limCone
F[⋁γ]Cone = limitC _ (F* (⋁ γ)) .limCone
F[⋁β∧⋁γ]Cone = limitC _ (F* (⋁ β ∧l ⋁ γ)) .limCone
F[⋁β++γ]Cone = limitC _ (F* (⋁ (β ++Fin γ))) .limCone
F[⋁β]Cone = limitC _ (F* (⋁ β)) .limCone
F[⋁γ]Cone = limitC _ (F* (⋁ γ)) .limCone
F[⋁β∧⋁γ]Cone = limitC _ (F* (⋁ β ∧l ⋁ γ)) .limCone
F[⋁β++γ]Cone = limitC _ (F* (⋁ (β ++Fin γ))) .limCone

-- the family of squares we need to construct cones over β++γ
to++ConeSquare : {c : ob C} (f : C [ c , ⋁Cospan .l ]) (g : C [ c , ⋁Cospan .r ])
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2 changes: 1 addition & 1 deletion Cubical/Experiments/ZCohomologyOld/Properties.agda
Original file line number Diff line number Diff line change
Expand Up @@ -268,12 +268,12 @@ cancelₖ (suc (suc (suc (suc (suc n))))) x = cong (ΩKn+1→Kn (5 + n)) (rCance
∙∙ cong (ΩKn+1→Kn (suc n)) (sym (rUnit (Kn→ΩKn+1 (suc n) x)))
∙∙ Iso.leftInv (Iso-Kn-ΩKn+1 (suc n)) x

open Iso renaming (inv to inv')
abstract
isCommΩK1 : (n : ℕ) → isComm∙ ((Ω^ n) (coHomK-ptd 1))
isCommΩK1 zero = isCommA→isCommTrunc 2 comm-ΩS¹ isGroupoidS¹
isCommΩK1 (suc n) = EH n

open Iso renaming (inv to inv')
isCommΩK : (n : ℕ) → isComm∙ (coHomK-ptd n)
isCommΩK zero p q = isSetℤ _ _ (p ∙ q) (q ∙ p)
isCommΩK (suc zero) = isCommA→isCommTrunc 2 comm-ΩS¹ isGroupoidS¹
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