Theorems · Theorem · category theory
TopCat.Presheaf.ext
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : TopCat} {P Q : TopCat.Presheaf C X} {f g : P ⟶ Q},
(∀ (U : TopologicalSpace.Opens ↑X), f.app (Opposite.op U) = g.app (Opposite.op U)) → f = g- Defined in
- Mathlib.Topology.Sheaves.Presheaf
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 30 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.
Cites10
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- TopCat.Presheafstatement and proof · cited by 371
- CategoryTheory.NatTrans.extproof · cited by 20
Cited by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.SheafedSpace.hom_stalk_extproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.copyBase_eqproof · cited by 1
- AlgebraicGeometry.Spec.sheafedSpaceMap_compproof · cited by 1
- AlgebraicGeometry.Spec.sheafedSpaceMap_idproof · cited by 1
- TopCat.Presheaf.ext_iffproof · cited by 0
- AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_facproof · cited by 0
- SkyscraperPresheafFunctor.map'_compproof · cited by 0
- SkyscraperPresheafFunctor.map'_idproof · cited by 0
- AlgebraicGeometry.PresheafedSpace.ofRestrict_top_cproof · cited by 0
- IsOpenMap.pullbackObjIso_hom_naturalityproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.extproof · cited by 0