File: Mathlib/AlgebraicGeometry/GluingOneHypercover.lean

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_f
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: D.oneHypercover.f i = D.ι i

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_p₁
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: ∀ (x : PUnit.{u + 1}), D.oneHypercover.p₁ x = D.f i₁ i₂

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_X
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: ∀ (a : D.J), D.oneHypercover.X a = D.U a

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_Y
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: ∀ (x : PUnit.{u + 1}), D.oneHypercover.Y x = D.V (i₁, i₂)

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_p₂
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: D.oneHypercover.p₂ j = D.t i₁ i₂ ≫ D.f i₂ i₁

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_I₀
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: D.oneHypercover.I₀ = D.J

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover_I₁
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: ∀ (x x_1 : D.J), D.oneHypercover.I₁ x x_1 = PUnit.{u + 1}

full_name: AlgebraicGeometry.Scheme.GlueData.oneHypercover
code: /-- The 1-hypercover of `D.glued` in the big Zariski site that is given by the
open cover `D.U` from the glue data `D`.
The "covering of the intersection of two such open subsets" is the trivial
covering given by `D.V`. -/
@[simps]
noncomputable def oneHypercover : Scheme.zariskiTopology.OneHypercover D.glued 
goal: AlgebraicGeometry.Scheme.zariskiTopology.OneHypercover D.glued

full_name: AlgebraicGeometry.Scheme.GlueData.sheafValGluedMk
code: /-- Constructor for sections over `D.glued` of a sheaf of types on the big Zariski site. -/
noncomputable def sheafValGluedMk : F.val.obj (op D.glued) 
goal: F.val.obj (Opposite.op D.glued)

full_name: AlgebraicGeometry.Scheme.GlueData.sheafValGluedMk_val
code: @[simp]
lemma sheafValGluedMk_val (j : D.J) : F.val.map (D.ι j).op (D.sheafValGluedMk s h) = s j 
goal: F.val.map (D.ι j).op (D.sheafValGluedMk s h) = s j