Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.Point.fiber
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{J : CategoryTheory.GrothendieckTopology C} → J.Point → CategoryTheory.Functor C (Type w)the fiber functor on the underlying category of the site
- Defined in
- Mathlib.CategoryTheory.Sites.Point.Basic
- Cited by
- 93 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 53 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Functorstatement · cited by 16,252
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.GrothendieckTopology.Pointstatement and proof · cited by 123
Cited by125
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.Point.presheafFiberproof · cited by 89
- CategoryTheory.GrothendieckTopology.Point.toPresheafFiberstatement and proof · cited by 46
- CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquivproof · cited by 18
- CategoryTheory.GrothendieckTopology.Point.mapproof · cited by 15
- CategoryTheory.GrothendieckTopology.Point.Hom.homstatement · cited by 12
- CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMapstatement and proof · cited by 12
- CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafFunctorproof · cited by 8
- CategoryTheory.GrothendieckTopology.Point.presheafFiberDescstatement and proof · cited by 7
- CategoryTheory.GrothendieckTopology.Point.jointly_surjectivestatement · cited by 6
- CategoryTheory.GrothendieckTopology.Point.presheafFiberCompIsoproof · cited by 6
- CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDescstatement and proof · cited by 6
- CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_extstatement and proof · cited by 5