Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.app_eq_appLE

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {U : Y.Opens},
  AlgebraicGeometry.Scheme.Hom.app f U =
    AlgebraicGeometry.Scheme.Hom.appLE f U ((TopologicalSpace.Opens.map f.base).obj U) ⋯

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 32 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites23

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 and proof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
Oppositestatement · cited by 8,081
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
CategoryTheory.Category.comp_idproof · cited by 2,119
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892

Cited by32

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
AlgebraicGeometry.Scheme.Hom.comp_appLEproof · cited by 7
AlgebraicGeometry.Scheme.Hom.normalizationDesc_compproof · cited by 5
AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturalityproof · cited by 4
AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkproof · cited by 3
AlgebraicGeometry.HasRingHomProperty.appTopproof · cited by 3
AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersionproof · cited by 2
AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalkproof · cited by 2
AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
AlgebraicGeometry.exists_app_map_eq_zero_of_isLimitproof · cited by 2