Theorems · Theorem · category theory
GrpCat.ker_eq_bot_of_mono
∀ {A B : GrpCat} (f : A ⟶ B) [CategoryTheory.Mono f], (GrpCat.Hom.hom f).ker = ⊥- Defined in
- Mathlib.Algebra.Category.Grp.EpiMono
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Mono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 4,720
- MonoidHomproof · cited by 3,629
- Subgroupstatement · cited by 3,593
- CategoryTheory.Monostatement and proof · cited by 893
- MonoidHom.compproof · cited by 469
- CategoryTheory.cancel_monoproof · cited by 435
- MonoidHom.kerstatement and proof · cited by 212
- GrpCatstatement and proof · cited by 146
- GrpCat.carrierstatement and proof · cited by 125
- CategoryTheory.ConcreteCategory.extproof · cited by 107
- GrpCat.Hom.homstatement and proof · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- GrpCat.mono_iff_ker_eq_botproof · cited by 1