Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsAffineHom
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes X ⟶ Y is affine if
the preimage of any affine open subset of Y is affine.
- Cited by
- 63 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 by77
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.preimagestatement and proof · cited by 17
- AlgebraicGeometry.isAffine_of_isAffineHomstatement and proof · cited by 9
- AlgebraicGeometry.exists_map_eq_topstatement and proof · cited by 5
- AlgebraicGeometry.ExistsHomHomCompEqCompAux.i'statement and proof · cited by 4
- AlgebraicGeometry.IsAffineHom.of_compstatement and proof · cited by 3
- AlgebraicGeometry.exists_map_preimage_le_map_preimagestatement and proof · cited by 3
- AlgebraicGeometry.isAffineHom_π_appstatement and proof · cited by 3
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomstatement and proof · cited by 2
- AlgebraicGeometry.IsAffineHom.isAffine_preimagestatement and proof · cited by 2
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitstatement and proof · cited by 2
- AlgebraicGeometry.exists_app_map_eq_zero_of_isLimitstatement and proof · cited by 2
- AlgebraicGeometry.exists_mem_of_isClosed_of_nonempty'statement and proof · cited by 2