Theorems · Theorem · category theory
ModuleCat.mono_iff_ker_eq_bot
∀ {R : Type u} [inst : Ring R] {X Y : ModuleCat R} (f : X ⟶ Y), CategoryTheory.Mono f ↔ (ModuleCat.Hom.hom f).ker = ⊥- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
Cites15
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.Homstatement and proof · cited by 32,603
- RingHom.idstatement · cited by 18,349
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement · cited by 997
- CategoryTheory.Monostatement and proof · cited by 893
- LinearMap.kerstatement and proof · cited by 848
- ModuleCat.Hom.homstatement and proof · cited by 341
Cited by1
Results whose statement or proof uses this declaration.
- ModuleCat.mono_iff_injectiveproof · cited by 21