Theorems · Inductive type · category theory
CategoryTheory.Functor.PreservesEpimorphisms
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → PropA functor preserves epimorphisms if it maps epimorphisms to epimorphisms.
- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
Cited by48
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.preservesEpimorphisms_of_preserves_of_reflectsstatement and proof · cited by 4
- CategoryTheory.Functor.preservesFiniteColimits_tfaeproof · cited by 4
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernelproof · cited by 3
- CategoryTheory.Functor.epi_map_iff_epistatement and proof · cited by 3
- CategoryTheory.Projective.projective_iff_preservesEpimorphisms_coyoneda_objstatement and proof · cited by 3
- CategoryTheory.Functor.preservesHomology_of_map_exactproof · cited by 2
- CategoryTheory.isInternallyProjectiveproof · cited by 2
- CategoryTheory.Injective.injective_iff_preservesEpimorphisms_yoneda_objstatement and proof · cited by 2
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesEpimorphismsstatement · cited by 2
- CategoryTheory.JointlyReflectEpimorphisms.epi_iffstatement and proof · cited by 2
- CategoryTheory.Adjunction.map_projectivestatement and proof · cited by 2
- CategoryTheory.Functor.PreservesEpimorphisms.iso_iffstatement and proof · cited by 2