Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.exists_of_trans_eq_trans

∀ {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] {i j k : 𝒰.I₀} (fi : i ⟶ k) (fj : j ⟶ k)
  (xi : ↥(𝒰.X i)) (xj : ↥(𝒰.X j)),
  (𝒰.trans fi) xi = (𝒰.trans fj) xj → ∃ l fli flj x, (𝒰.trans fli) x = xi ∧ (𝒰.trans flj) x = xj

Defined in

Mathlib.AlgebraicGeometry.Cover.Directed

Cited by

0 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.Scheme.Cover.LocallyDirected