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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.toLRSHom

{X Y : AlgebraicGeometry.Scheme} → X.Hom Y → (X.toLocallyRingedSpace ⟶ Y.toLocallyRingedSpace)

Cast a morphism of schemes into morphisms of local ringed spaces.

Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
58 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.IsOpenImmersion · cited by 476AlgebraicGeometry.IsOpenI…AlgebraicGeometry.Scheme.Hom.opensFunctor · cited by 204Hom.opensFunctorAlgebraicGeometry.Scheme.Hom.stalkMap · cited by 82Hom.stalkMapAlgebraicGeometry.Scheme.Hom.appIso · cited by 48Hom.appIsoAlgebraicGeometry.IsOpenImmersion.lift · cited by 20IsOpenImmersion.liftAlgebraicGeometry.IsOpenImmersion.lift_fac · cited by 18IsOpenImmersion.lift_facAlgebraicGeometry.Scheme.forgetToLocallyRingedSpace · cited by 17Scheme.forgetToLocallyRin…AlgebraicGeometry.Scheme.preimage_basicOpen · cited by 16Scheme.preimage_basicOpenAlgebraicGeometry.Scheme.Hom.support_ker · cited by 6Hom.support_kerAlgebraicGeometry.Scheme.Hom.ext' · cited by 5Hom.ext'AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso · cited by 4Hom.opensRange_of_isIsoAlgebraicGeometry.Scheme.Hom.appIso_inv_naturality · cited by 4Hom.appIso_inv_naturalityAlgebraicGeometry.HasRingHomProperty.of_comp · cited by 3HasRingHomProperty.of_compAlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom · cited by 3Hom.stalkMap_congr_homAlgebraicGeometry.IsOpenImmersion.image_preimage_eq_preimage_image_of_isPullback · cited by 3IsOpenImmersion.image_pre…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Hom.toLRSHom' · cited by 895Hom.toLRSHom'AlgebraicGeometry.LocallyRingedSpace · cited by 205AlgebraicGeometry.Locally…AlgebraicGeometry.Scheme.Hom · cited by 35Scheme.HomHom.toLRSHomCITED BYCITES

Cites6

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

Cited by66

Results whose statement or proof uses this declaration.