Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.intersectionOfLocallyDirected_f

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {X : AlgebraicGeometry.Scheme}
  (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X)
  [inst : CategoryTheory.Category.{v_1, u_1} 𝒰.I₀] [inst_1 : 𝒰.LocallyDirected] [inst_2 : P.IsStableUnderBaseChange]
  [inst_3 : P.HasOfPostcompProperty P] (i j : 𝒰.I₀) (k : (k : 𝒰.I₀) × (k ⟶ i) × (k ⟶ j)),
  (𝒰.intersectionOfLocallyDirected i j).f k = CategoryTheory.Limits.pullback.lift (𝒰.trans k.snd.1) (𝒰.trans k.snd.2) ⋯

Defined in

Mathlib.AlgebraicGeometry.Cover.Directed

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.Scheme.Cover.LocallyDirectedCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.HasOfPostcompProperty