Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.homOfLE_base
∀ {X : AlgebraicGeometry.Scheme} {U V : X.Opens} (e : U ≤ V),
(X.homOfLE e).base = (TopologicalSpace.Opens.toTopCat ↑X.toPresheafedSpace).map (CategoryTheory.homOfLE e)- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · 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 and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictproof · cited by 2
- AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpenproof · cited by 2
- AlgebraicGeometry.Scheme.homOfLE_apply'proof · cited by 2