Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isoImage_preimage_hom_homOfLE_assoc
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.IsOpenImmersion f] (U : Y.Opens)
{Z : AlgebraicGeometry.Scheme} (h : ↑U ⟶ Z),
CategoryTheory.CategoryStruct.comp
(AlgebraicGeometry.Scheme.Hom.isoImage f ((TopologicalSpace.Opens.map f.base).obj U)).hom
(CategoryTheory.CategoryStruct.comp (Y.homOfLE ⋯) h) =
CategoryTheory.CategoryStruct.comp (f ∣_ U) h- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites25
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
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- 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
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