Theorems · Theorem · category theory
AddCommGrpCat.epi_iff_surjective
∀ {A B : AddCommGrpCat} (f : A ⟶ B), CategoryTheory.Epi f ↔ Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)- Defined in
- Mathlib.Algebra.Category.Grp.EpiMono
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddMonoidHomstatement · cited by 3,230
- CategoryTheory.Epistatement · cited by 688
- AddCommGrpCatstatement and proof · cited by 462
- AddCommGrpCat.carrierstatement · cited by 407
- AddMonoidHom.range_eq_topproof · cited by 20
- AddCommGrpCat.epi_iff_range_eq_topproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- TopCat.Sheaf.IsFlasque.epi_of_shortExactproof · cited by 1
- CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjectiveproof · cited by 1
- CategoryTheory.ShortComplex.exact_iff_surjective_abToCyclesproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.ab_surjective_gproof · cited by 1
- CategoryTheory.Preadditive.epi_iff_surjectiveproof · cited by 1