Theorems · Definition · algebraic geometry
AlgebraicGeometry.PresheafedSpace.ofRestrict
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{U : TopCat} →
(X : AlgebraicGeometry.PresheafedSpace C) →
{f : U ⟶ ↑X} → (h : Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f)) → X.restrict h ⟶ XThe map from the restriction of a presheafed space.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositeproof · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- Opposite.unopproof · cited by 2,231
- TopologicalSpace.Opensproof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
Cited by18
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.restrictproof · cited by 10
- AlgebraicGeometry.LocallyRingedSpace.ofRestrictproof · cited by 10
- AlgebraicGeometry.SheafedSpace.ofRestrictproof · cited by 8
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invAppstatement and proof · cited by 4
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftproof · cited by 3
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement and proof · cited by 3
- AlgebraicGeometry.PresheafedSpace.restrictTopIsoproof · cited by 2
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrictstatement · cited by 2
- AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_ofRestrictstatement and proof · cited by 1
- AlgebraicGeometry.SheafedSpace.restrictTopIso_homstatement · cited by 0
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp_applystatement · cited by 0
- AlgebraicGeometry.PresheafedSpace.ofRestrict_basestatement and proof · cited by 0