Theorems · Theorem · algebraic geometry
AlgebraicGeometry.ext_of_isDominant_of_isSeparated
∀ {W X Y Z : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsReduced X] {f g : X ⟶ Y} (s : Y ⟶ Z)
[AlgebraicGeometry.IsSeparated s],
CategoryTheory.CategoryStruct.comp f s = CategoryTheory.CategoryStruct.comp g s →
∀ (ι : W ⟶ X) [AlgebraicGeometry.IsDominant ι],
CategoryTheory.CategoryStruct.comp ι f = CategoryTheory.CategoryStruct.comp ι g → f = gSuppose X is a reduced scheme and that f g : X ⟶ Y agree over some separated Y ⟶ Z.
Then f = g if ι ≫ f = ι ≫ g for some dominant ι.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
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- CategoryTheory.cancel_epiproof · cited by 380
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- CategoryTheory.Over.Hom.leftproof · cited by 287
- CategoryTheory.Over.mkproof · cited by 203
- CategoryTheory.Over.homMkproof · cited by 115
- CategoryTheory.Limits.equalizer.ιproof · cited by 64
- AlgebraicGeometry.Surjectiveproof · cited by 48
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ext_of_fromSpecResidueField_eqproof · cited by 1
- AlgebraicGeometry.ext_of_isDominantproof · cited by 1
- AlgebraicGeometry.ext_of_isDominant_of_isSeparated'proof · cited by 1