Theorems · Theorem · category theory
CommGrpCat.mono_iff_ker_eq_bot
∀ {A B : CommGrpCat} (f : A ⟶ B), CategoryTheory.Mono f ↔ (CommGrpCat.Hom.hom f).ker = ⊥- Defined in
- Mathlib.Algebra.Category.Grp.EpiMono
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Quiver.Homstatement and proof · cited by 32,603
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement · cited by 3,593
- CategoryTheory.Monostatement and proof · cited by 893
- MonoidHom.kerstatement and proof · cited by 212
- CommGrpCatstatement and proof · cited by 74
- CommGrpCat.carrierstatement · cited by 59
- CommGrpCat.Hom.homstatement and proof · cited by 26
- MonoidHom.ker_eq_bot_iffproof · cited by 16
- CategoryTheory.ConcreteCategory.mono_of_injectiveproof · cited by 12
- CommGrpCat.ker_eq_bot_of_monoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CommGrpCat.mono_iff_injectiveproof · cited by 0