Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed

∀ {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} [self : 𝒰.LocallyDirected] {i j : 𝒰.I₀}
  (x : ↥(CategoryTheory.Limits.pullback (𝒰.f i) (𝒰.f j))),
  ∃ k hki hkj y,
    (CategoryTheory.Limits.pullback.lift (AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans hki)
          (AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans hkj) ⋯)
        y =
      x

Defined in

Mathlib.AlgebraicGeometry.Cover.Directed

Cited by

1 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.Scheme.Cover.LocallyDirected