Theorems · Theorem · category theory
GrpCat.mono_iff_injective
∀ {A B : GrpCat} (f : A ⟶ B), CategoryTheory.Mono f ↔ Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f)- Defined in
- Mathlib.Algebra.Category.Grp.EpiMono
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- MonoidHomstatement · cited by 3,629
- CategoryTheory.Monostatement · cited by 893
- GrpCatstatement and proof · cited by 146
- GrpCat.carrierstatement · cited by 125
- GrpCat.Hom.homproof · cited by 47
- MonoidHom.ker_eq_bot_iffproof · cited by 16
- GrpCat.mono_iff_ker_eq_botproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ProfiniteGrp.ProfiniteCompletion.mono_eta_iff_residuallyFiniteproof · cited by 1
- ProfiniteGrp.ProfiniteCompletion.etaFn_injective_iff_residuallyFiniteproof · cited by 0