Theorems · Theorem · algebraic geometry
AlgebraicGeometry.mem_range_iff_of_surjective
∀ {X Y S : AlgebraicGeometry.Scheme} (f : X ⟶ S) (g : Y ⟶ S) (e : X ⟶ Y) [AlgebraicGeometry.Surjective e],
CategoryTheory.CategoryStruct.comp e g = f → ∀ (s : ↥S), s ∈ Set.range ⇑f ↔ s ∈ Set.range ⇑g- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.Surjective
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
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