Mathlib Map

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 ⟶ X

The map from the restriction of a presheafed space.

Defined in
Mathlib.Geometry.RingedSpace.PresheafedSpace
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.

AlgebraicGeometry.Scheme.restrict · cited by 10Scheme.restrictAlgebraicGeometry.LocallyRingedSpace.ofRestrict · cited by 10LocallyRingedSpace.ofRest…AlgebraicGeometry.SheafedSpace.ofRestrict · cited by 8SheafedSpace.ofRestrictAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp · cited by 4IsOpenImmersion.ofRestric…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeft · cited by 3IsOpenImmersion.pullbackC…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict · cited by 3IsOpenImmersion.isoRestri…AlgebraicGeometry.PresheafedSpace.restrictTopIso · cited by 2PresheafedSpace.restrictT…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict · cited by 2IsOpenImmersion.isoRestri…AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_ofRestrict · cited by 1PresheafedSpace.restrictS…AlgebraicGeometry.SheafedSpace.restrictTopIso_hom · cited by 0SheafedSpace.restrictTopI…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invApp_apply · cited by 0IsOpenImmersion.ofRestric…AlgebraicGeometry.PresheafedSpace.ofRestrict_base · cited by 0PresheafedSpace.ofRestric…AlgebraicGeometry.PresheafedSpace.ofRestrict_c_app · cited by 0PresheafedSpace.ofRestric…AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c · cited by 0PresheafedSpace.ofRestric…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_cone_of_left_condition · cited by 0IsOpenImmersion.pullback_…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierContinuousMap · cited by 2491ContinuousMapOpposite.unop · cited by 2231Opposite.unopTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierQuiver.Hom.op · cited by 1948Hom.opTopCat · cited by 1889TopCatAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafPresheafedSpace.ofRestrictCITED BYCITES

Cites20

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.