Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_left
∀ {X Y Z : AlgebraicGeometry.Scheme} [inst : PreirreducibleSpace ↥X] [inst_1 : Nonempty ↥Y] {f₁ f₂ : X.PartialMap Y}
[inst_2 : AlgebraicGeometry.IsDominant f₁.hom] [inst_3 : AlgebraicGeometry.IsDominant f₂.hom],
f₁.equiv f₂ → ∀ (g : Y.PartialMap Z), (f₁.comp g).equiv (f₂.comp g)Composition respects equivalence of partial maps on the left.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CategoryTheory.Category.id_compproof · cited by 1,998
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.RationalMap.toRationalMap_compproof · cited by 1
- AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equivproof · cited by 0
- AlgebraicGeometry.Scheme.RationalMap.comp_assocproof · cited by 0