Theorems · Definition · algebraic geometry
AlgebraicGeometry.SheafedSpace.ofRestrict
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{U : TopCat} →
(X : AlgebraicGeometry.SheafedSpace C) →
{f : U ⟶ ↑X.toPresheafedSpace} →
(h : Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f)) → X.restrict h ⟶ XThe map from the restriction of a presheafed space.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 90 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.
Cites14
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.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- TopCatstatement and proof · cited by 1,889
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- AlgebraicGeometry.SheafedSpacestatement and proof · cited by 142
- CategoryTheory.InducedCategory.homMkproof · cited by 33
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement · cited by 2
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invAppstatement · cited by 1
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrictstatement · cited by 1
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict_invApp_applystatement · cited by 0
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assocstatement and proof · cited by 0
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assocstatement and proof · cited by 0
- AlgebraicGeometry.SheafedSpace.ofRestrict_hom_basestatement and proof · cited by 0
- AlgebraicGeometry.SheafedSpace.ofRestrict_hom_c_appstatement and proof · cited by 0