Theorems · Definition · category theory
CategoryTheory.Sheaf.finestTopology
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
Set (CategoryTheory.Functor Cᵒᵖ (Type w)) → CategoryTheory.GrothendieckTopology CConstruct the finest (largest) Grothendieck topology for which all the given presheaves are sheaves.
- Defined in
- Mathlib.CategoryTheory.Sites.Canonical
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 36 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Set.imageproof · cited by 5,609
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- InfSet.sInfproof · cited by 935
- CategoryTheory.Sheaf.finestTopologySingleproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.inducedTopologyproof · cited by 19
- CategoryTheory.Sheaf.canonicalTopologyproof · cited by 5
- CategoryTheory.Sheaf.mem_finestTopology_of_forall_isSheafForstatement · cited by 2
- CategoryTheory.Sheaf.le_finestTopologystatement · cited by 2
- CategoryTheory.Sheaf.sheaf_for_finestTopologystatement and proof · cited by 1