Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.IsLocalSite.point
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(J : CategoryTheory.GrothendieckTopology C) → [CategoryTheory.LocallySmall.{w, v, u} C] → [J.IsLocalSite] → J.PointEvery local site has a canonical point, given as a fibre functor by the coyoneda embedding of
the terminal object ⊤_ C.
- Defined in
- Mathlib.CategoryTheory.Sites.LocalSite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.LocallySmallstatement and proof · cited by 242
- CategoryTheory.Limits.terminalproof · cited by 141
- CategoryTheory.GrothendieckTopology.Pointstatement · cited by 123
- CategoryTheory.shrinkCoyonedaproof · cited by 23
- CategoryTheory.GrothendieckTopology.IsLocalSitestatement and proof · cited by 10
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIsostatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.IsLocalSite.toPresheafFiber_pointPresheafFiberIso_homstatement and proof · cited by 2
- CategoryTheory.GrothendieckTopology.IsLocalSite.toPresheafFiber_pointPresheafFiberIso_hom_assocstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.IsLocalSite.ΓCoconstantSheafAdjproof · cited by 1
- CategoryTheory.GrothendieckTopology.IsLocalSite.coconstantSheafproof · cited by 1
- CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIso_naturalitystatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.IsLocalSite.coconstantSheafΓNatIsoIdproof · cited by 0
- CategoryTheory.GrothendieckTopology.IsLocalSite.point.congr_simpstatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIso_naturality_assocstatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberNatIsostatement · cited by 0
- CategoryTheory.GrothendieckTopology.IsLocalSite.pointSheafFiberIsostatement · cited by 0