Theorems · Theorem · category theory
ModuleCat.epi_iff_surjective
∀ {R : Type u} [inst : Ring R] {X Y : ModuleCat R} (f : X ⟶ Y),
CategoryTheory.Epi f ↔ Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement · cited by 997
- CategoryTheory.Epistatement · cited by 688
- LinearMap.range_eq_topproof · cited by 107
- ModuleCat.epi_iff_range_eq_topproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Rep.epi_iff_surjectiveproof · cited by 3
- groupHomology_induction_onproof · cited by 3
- groupCohomology_induction_onproof · cited by 2
- PresheafOfModules.surjective_of_epiproof · cited by 1
- CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequalproof · cited by 0
- ModuleCat.span_rightExactproof · cited by 0
- ModuleCat.linearIndependent_shortExactproof · cited by 0