Theorems · Definition · category theory
TopCat.Sheaf.presheaf
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X : TopCat} → TopCat.Sheaf C X → TopCat.Presheaf C XThe underlying presheaf of a sheaf
- Defined in
- Mathlib.Topology.Sheaves.Sheaf
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 74 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.
Cites5
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
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- TopCat.Presheafstatement · cited by 371
- TopCat.Sheafstatement and proof · cited by 73
Cited by104
Results whose statement or proof uses this declaration.
- smoothSheafCommRing.evalHomstatement and proof · cited by 13
- smoothSheafCommRing.forgetStalkstatement and proof · cited by 13
- AlgebraicGeometry.tilde.toOpenstatement · cited by 10
- smoothSheaf.evalHomstatement · cited by 9
- AlgebraicGeometry.Scheme.Modules.fromTildeΓstatement and proof · cited by 9
- TopCat.Presheaf.section_extstatement and proof · cited by 7
- AlgebraicGeometry.Proj.stalkIso'statement and proof · cited by 7
- AlgebraicGeometry.tilde.toOpen_resstatement · cited by 4
- AlgebraicGeometry.stalkToFiberRingHomstatement · cited by 4
- TopCat.stalkToFiberstatement · cited by 4
- smoothSheafCommRing.evalstatement · cited by 4
- smoothSheafCommRing.ι_evalHomstatement · cited by 4