Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.exists_of_f_eq_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] {i j : 𝒰.I₀} (xi : ↥(𝒰.X i))
(xj : ↥(𝒰.X j)), (𝒰.f i) xi = (𝒰.f j) xj → ∃ k fi fj xk, (𝒰.trans fi) xk = xi ∧ (𝒰.trans fj) xk = xj- Defined in
- Mathlib.AlgebraicGeometry.Cover.Directed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.exists_of_trans_eq_transproof · cited by 0