Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.Surjective
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes is surjective if the underlying map is.
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by51
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.surjectivestatement and proof · cited by 12
- AlgebraicGeometry.Scheme.Hom.coverstatement and proof · cited by 8
- AlgebraicGeometry.surjective_iffstatement and proof · cited by 6
- AlgebraicGeometry.Surjective.surjstatement and proof · cited by 5
- AlgebraicGeometry.range_eq_univstatement and proof · cited by 4
- AlgebraicGeometry.ext_of_isDominant_of_isSeparatedproof · cited by 3
- AlgebraicGeometry.Scheme.Hom.presieve₀_coverstatement and proof · cited by 2
- AlgebraicGeometry.isIso_iff_isOpenImmersion_and_surjectivestatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.singleton_mem_propQCPrecoveragestatement and proof · cited by 2
- AlgebraicGeometry.universallyInjective_eq_diagonalstatement and proof · cited by 2
- AlgebraicGeometry.UniversallyClosed.of_comp_surjectivestatement and proof · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompactstatement and proof · cited by 2