Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.Point.Hom.hom
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{J : CategoryTheory.GrothendieckTopology C} → {Φ₁ Φ₂ : J.Point} → Φ₁.Hom Φ₂ → (Φ₂.fiber ⟶ Φ₁.fiber)a natural transformation, in the opposite direction
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 20 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.
Cites7
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.GrothendieckTopology.Pointstatement and proof · cited by 123
- CategoryTheory.GrothendieckTopology.Point.fiberstatement · cited by 93
- CategoryTheory.GrothendieckTopology.Point.Homstatement and proof · cited by 5
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiberproof · cited by 4
- CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_appstatement · cited by 3
- CategoryTheory.GrothendieckTopology.Point.Hom.extstatement and proof · cited by 2
- CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_compproof · cited by 2
- CategoryTheory.GrothendieckTopology.Point.comp_homstatement · cited by 1
- CategoryTheory.GrothendieckTopology.Point.hom_extstatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_idproof · cited by 1
- CategoryTheory.GrothendieckTopology.Point.Hom.sheafFiber_compproof · cited by 1
- CategoryTheory.GrothendieckTopology.pointBotFunctor_map_homstatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.Point.comp_hom_assocstatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.Point.hom_ext_iffstatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.Point.id_homstatement · cited by 0