Theorems · Theorem · category theory
CategoryTheory.Functor.epi_of_epi_map
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) [F.ReflectsEpimorphisms] {X Y : C} {f : X ⟶ Y},
CategoryTheory.Epi (F.map f) → CategoryTheory.Epi f- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 8,698
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Functor.ReflectsEpimorphismsstatement and proof · cited by 9
- CategoryTheory.Functor.ReflectsEpimorphisms.reflectsproof · cited by 1
Cited by24
Results whose statement or proof uses this declaration.
- TopCat.epi_iff_surjectiveproof · cited by 11
- CategoryTheory.ConcreteCategory.epi_of_surjectiveproof · cited by 9
- CategoryTheory.Functor.preservesEpimorphisms_of_preserves_of_reflectsproof · cited by 4
- Rep.epi_iff_surjectiveproof · cited by 3
- LightProfinite.epi_iff_surjectiveproof · cited by 3
- CategoryTheory.Functor.epi_map_iff_epiproof · cited by 3
- Profinite.epi_iff_surjectiveproof · cited by 2
- CompHaus.epi_iff_surjectiveproof · cited by 2
- CategoryTheory.Functor.ReflectsEpimorphisms.of_isoproof · cited by 2
- AlgebraicGeometry.Flat.epi_of_flat_of_surjectiveproof · cited by 1
- AddGrpCat.epi_iff_surjectiveproof · cited by 1
- CategoryTheory.CostructuredArrow.epi_of_epi_leftproof · cited by 1