Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.comp_appLE
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U : Z.Opens) (V : X.Opens)
(e : V ≤ (TopologicalSpace.Opens.map (CategoryTheory.CategoryStruct.comp f g).base).obj U),
AlgebraicGeometry.Scheme.Hom.appLE (CategoryTheory.CategoryStruct.comp f g) U V e =
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.app g U)
(AlgebraicGeometry.Scheme.Hom.appLE f ((TopologicalSpace.Opens.map g.base).obj U) V e)- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.compstatement and proof · 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
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimageproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_iSup_eq_topproof · cited by 1
- AlgebraicGeometry.sourceAffineLocally_respectsIsoproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.comp_appLE_assocproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.normalization.hom_extproof · cited by 0
- AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_compproof · cited by 0
- AlgebraicGeometry.FormallyUnramified.hom_extproof · cited by 0