Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHom
∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y},
AlgebraicGeometry.IsIntegralHom f ↔ AlgebraicGeometry.UniversallyClosed f ∧ AlgebraicGeometry.IsAffineHom f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites51
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Algebraproof · cited by 11,388
- Top.topproof · cited by 9,680
- CategoryTheory.Iso.invproof · cited by 6,514
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatproof · cited by 2,333
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIntegral_appTop_of_universallyClosedproof · cited by 1
- AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHomproof · cited by 1