Theorems · Theorem · category theory
CategoryTheory.GrothendieckTopology.Point.fiber_map_injective_of_mono
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} (Φ : J.Point)
[CategoryTheory.LocallySmall.{w, v, u} C] {U T : C} (f : U ⟶ T) [CategoryTheory.Mono f],
Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (Φ.fiber.map f))- Defined in
- Mathlib.CategoryTheory.Sites.Point.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.LocallySmallstatement and proof · cited by 242
- CategoryTheory.GrothendieckTopology.Pointstatement and proof · cited by 123
- CategoryTheory.GrothendieckTopology.Point.fiberstatement and proof · cited by 93
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.Point.subsingleton_fiber_objproof · cited by 0