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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.

AlgebraicGeometry.affineAnd · cited by 21AlgebraicGeometry.affineA…AlgebraicGeometry.HasRingHomProperty.Spec_iff · cited by 19HasRingHomProperty.Spec_i…AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv · cited by 12AffineSpace.toSpecMvPolyI…AlgebraicGeometry.Scheme.ΓSpecIso_naturality · cited by 11Scheme.ΓSpecIso_naturalityAlgebraicGeometry.AffineSpace.isoOfIsAffine · cited by 10AffineSpace.isoOfIsAffineAlgebraicGeometry.HasRingHomProperty.iff_of_isAffine · cited by 9HasRingHomProperty.iff_of…AlgebraicGeometry.Scheme.toSpecΓ_naturality · cited by 9Scheme.toSpecΓ_naturalityAlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec · cited by 8IsAffineOpen.SpecMap_appL…AlgebraicGeometry.AffineSpace.hom_ext · cited by 8AffineSpace.hom_extAlgebraicGeometry.Scheme.Hom.comp_appTop · cited by 7Hom.comp_appTopAlgebraicGeometry.Scheme.toSpecΓ_appTop · cited by 7Scheme.toSpecΓ_appTopAlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen · cited by 7Scheme.toSpecΓ_preimage_b…AlgebraicGeometry.Scheme.Hom.support_ker · cited by 6Hom.support_kerAlgebraicGeometry.arrowIsoΓSpecOfIsAffine · cited by 6AlgebraicGeometry.arrowIs…AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrank · cited by 6Hom.finrank_SpecMap_eq_fi…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objTop.top · cited by 9680Top.topOpposite · cited by 8081OppositeTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafAlgebraicGeometry.Scheme.Hom.app · cited by 176Hom.appHom.appTopCITED BYCITES

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by118

Results whose statement or proof uses this declaration.