Theorems · Theorem · category theory
CategoryTheory.Functor.ReflectsEpimorphisms.reflects
∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
{F : CategoryTheory.Functor C D} [self : F.ReflectsEpimorphisms] {X Y : C} (f : X ⟶ Y),
CategoryTheory.Epi (F.map f) → CategoryTheory.Epi fA functor reflects epimorphisms if morphisms that are mapped to epimorphisms are themselves epimorphisms.
- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Epistatement · cited by 688
- CategoryTheory.Functor.ReflectsEpimorphismsstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.epi_of_epi_mapproof · cited by 24