Theorems · Theorem · category theory
CategoryTheory.surjective_of_epi
∀ {X Y : Type u} (f : X ⟶ Y) [hf : CategoryTheory.Epi f], Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Epi
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.epi_iff_surjectiveproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Types.range_fst_of_isPullbackproof · cited by 2
- CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epiproof · cited by 1
- CategoryTheory.isSplitEpi_iff_surjectiveproof · cited by 0