Theorems · Theorem · category theory
CategoryTheory.ofHom_epi_iff_surjective
∀ {X Y : Type u} (f : X → Y), CategoryTheory.Epi (TypeCat.ofHom f) ↔ Function.Surjective fA morphism in Type _ is an epimorphism if and only if it is surjective.
- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Equiv.symmproof · cited by 3,681
- CategoryTheory.Epistatement and proof · cited by 688
- Equiv.injectiveproof · cited by 464
- TypeCat.ofHomstatement and proof · cited by 389
- CategoryTheory.comp_applyproof · cited by 387
- CategoryTheory.types_congr_homproof · cited by 149
- CategoryTheory.ConcreteCategory.congr_homproof · cited by 138
- Equiv.uliftproof · cited by 115
Cited by5
Results whose statement or proof uses this declaration.
- TopCat.epi_iff_surjectiveproof · cited by 11
- LightProfinite.epi_iff_surjectiveproof · cited by 3
- Profinite.epi_iff_surjectiveproof · cited by 2
- CompHaus.epi_iff_surjectiveproof · cited by 2
- CompHausLike.epi_of_surjectiveproof · cited by 0