Theorems · Inductive type · category theory
CategoryTheory.GrothendieckTopology.Subcanonical
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.GrothendieckTopology C → PropA subcanonical topology is a topology which is smaller than the canonical topology. Equivalently, a topology is subcanonical iff every representable is a sheaf.
- Defined in
- Mathlib.CategoryTheory.Sites.Canonical
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
Cited by71
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.yonedastatement and proof · cited by 37
- CategoryTheory.GrothendieckTopology.uliftYonedastatement and proof · cited by 23
- CategoryTheory.GrothendieckTopology.yonedaEquivstatement and proof · cited by 18
- CategoryTheory.GrothendieckTopology.uliftYonedaEquivstatement and proof · cited by 14
- CategoryTheory.GrothendieckTopology.Subcanonical.isSheaf_of_isRepresentablestatement and proof · cited by 5
- CategoryTheory.GrothendieckTopology.yonedaEquiv_compstatement and proof · cited by 5
- CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheafstatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyonedastatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_mapstatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.OneHypercover.glueMorphismsstatement and proof · cited by 3
- CategoryTheory.Precoverage.ZeroHypercover.glueMorphismsstatement and proof · cited by 3
- CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_mapstatement and proof · cited by 3