Theorems · Theorem · category theory
AddCommGrpCat.mono_iff_injective
∀ {A B : AddCommGrpCat} (f : A ⟶ B), CategoryTheory.Mono f ↔ Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f)- Defined in
- Mathlib.Algebra.Category.Grp.EpiMono
- Cited by
- 6 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
- AddMonoidHomstatement · cited by 3,230
- CategoryTheory.Monostatement · cited by 893
- AddCommGrpCatstatement and proof · cited by 462
- AddCommGrpCat.carrierstatement · cited by 407
- AddCommGrpCat.Hom.homproof · cited by 72
- AddMonoidHom.ker_eq_bot_iffproof · cited by 14
- AddCommGrpCat.mono_iff_ker_eq_botproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Preadditive.mono_iff_injectiveproof · cited by 3
- groupCohomology.cocyclesMk₁_eqproof · cited by 2
- CategoryTheory.ShortComplex.ShortExact.ab_injective_fproof · cited by 1
- groupCohomology.cocyclesMk₂_eqproof · cited by 1
- CategoryTheory.Abelian.Ext.mono_postcomp_mk₀_of_monoproof · cited by 0
- CategoryTheory.Abelian.Ext.mono_precomp_mk₀_of_epiproof · cited by 0