Theorems · Theorem · category theory
CategoryTheory.Functor.PreservesEpimorphisms.of_natTrans
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F G : CategoryTheory.Functor C D} [F.PreservesEpimorphisms] (f : F ⟶ G) [∀ (X : C), CategoryTheory.Epi (f.app X)],
G.PreservesEpimorphisms- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Functor.PreservesEpimorphismsstatement and proof · cited by 41
- CategoryTheory.epi_of_epiproof · cited by 10
- CategoryTheory.NatTrans.naturality'proof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.PreservesEpimorphisms.of_isoproof · cited by 2
- CategoryTheory.Functor.preservesEpimorphisms.of_natTransproof · cited by 0