Theorems · Theorem · category theory
CategoryTheory.epi_iff_surjective
∀ {X Y : Type u} (f : X ⟶ Y), CategoryTheory.Epi f ↔ Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)A morphism in Type is an epimorphism if and only if it is surjective.
- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Epistatement and proof · cited by 688
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.ConcreteCategory.epi_of_surjectiveproof · cited by 9
- CategoryTheory.surjective_of_epiproof · cited by 4
- SSet.hasDimensionLT_of_epiproof · cited by 2
- CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_mapproof · cited by 1
- CategoryTheory.GlueData.types_π_surjectiveproof · cited by 1
- CategoryTheory.ConcreteCategory.surjective_eq_epimorphisms_iffproof · cited by 1
- CategoryTheory.ConcreteCategory.surjective_le_epimorphismsproof · cited by 1
- CategoryTheory.ConcreteCategory.surjective_of_epi_of_preservesPushoutproof · cited by 0
- CategoryTheory.ConcreteCategory.epi_iff_surjective_of_preservesPushoutproof · cited by 0