Theorems · Theorem · category theory
ModuleCat.range_eq_top_of_epi
∀ {R : Type u} [inst : Ring R] {X Y : ModuleCat R} (f : X ⟶ Y) [CategoryTheory.Epi f], (ModuleCat.Hom.hom f).range = ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingCategoryTheory.Epi
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- RingHom.idstatement and proof · cited by 18,349
- LinearMapproof · cited by 10,215
- Top.topstatement · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- HasQuotient.Quotientproof · cited by 2,301
- LinearMap.compproof · cited by 1,642
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement and proof · cited by 997
- LinearMap.rangestatement and proof · cited by 893
- CategoryTheory.Epistatement and proof · cited by 688
Cited by2
Results whose statement or proof uses this declaration.
- ModuleCat.epi_iff_range_eq_topproof · cited by 1
- ModuleCat.normalEpiproof · cited by 0