Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.appTop
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → (Y.presheaf.obj (Opposite.op ⊤) ⟶ X.presheaf.obj (Opposite.op ⊤))Given a morphism of schemes f : X ⟶ Y, this is the induced map Γ(Y, ⊤) ⟶ Γ(X, ⊤).
This is treated as a suffix in lemma names.
- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 109 results in Mathlib
- Foundations
- Depth 100 from the axioms, rests on 1,349 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.objstatement · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by118
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.affineAndproof · cited by 21
- AlgebraicGeometry.HasRingHomProperty.Spec_iffproof · cited by 19
- AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquivproof · cited by 12
- AlgebraicGeometry.Scheme.ΓSpecIso_naturalitystatement · cited by 11
- AlgebraicGeometry.AffineSpace.isoOfIsAffineproof · cited by 10
- AlgebraicGeometry.HasRingHomProperty.iff_of_isAffinestatement and proof · cited by 9
- AlgebraicGeometry.Scheme.toSpecΓ_naturalitystatement · cited by 9
- AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
- AlgebraicGeometry.AffineSpace.hom_extstatement and proof · cited by 8
- AlgebraicGeometry.Scheme.Hom.comp_appTopstatement · cited by 7
- AlgebraicGeometry.Scheme.toSpecΓ_appTopstatement and proof · cited by 7
- AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpenproof · cited by 7