Theorems · Theorem · category theory
CategoryTheory.Functor.epi_map_iff_epi
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y) [hF₁ : F.PreservesEpimorphisms] [hF₂ : F.ReflectsEpimorphisms],
CategoryTheory.Epi (F.map f) ↔ CategoryTheory.Epi f- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · 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 and proof · cited by 688
- CategoryTheory.Functor.PreservesEpimorphismsstatement and proof · cited by 41
- CategoryTheory.Functor.epi_of_epi_mapproof · cited by 24
- CategoryTheory.Functor.ReflectsEpimorphismsstatement and proof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- SimplexCategory.epi_iff_surjectiveproof · cited by 5
- Condensed.epi_iff_surjective_on_stoneanproof · cited by 2
- CategoryTheory.ConcreteCategory.epi_iff_surjective_of_preservesPushoutproof · cited by 0