Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (X : AlgebraicGeometry.PresheafedSpace C),
  (X.restrict ⋯).presheaf =
    (TopCat.Presheaf.pushforward C (TopologicalSpace.Opens.inclusionTopIso ↑X).inv).obj X.presheaf

Defined in: Mathlib.Geometry.RingedSpace.PresheafedSpace
Cited by: 1 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites22

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

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorproof · cited by 16,252
Top.topstatement and proof · cited by 9,680
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.Iso.invstatement and proof · cited by 6,514
TopCat.carrierstatement and proof · cited by 3,184
TopologicalSpace.Opensstatement and proof · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
TopCatstatement · cited by 1,889
AlgebraicGeometry.PresheafedSpace.presheafstatement and proof · cited by 1,104
CategoryTheory.Functor.opproof · cited by 997

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.PresheafedSpace.toRestrictTopproof · cited by 4
AlgebraicGeometry.PresheafedSpace.toRestrictTop_cstatement · cited by 0