Theorems · Theorem · category theory
CategoryTheory.injective_of_mono
∀ {X Y : Type u} (f : X ⟶ Y) [hf : CategoryTheory.Mono f], Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f)- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Mono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.mono_iff_injectiveproof · cited by 20
Cited by14
Results whose statement or proof uses this declaration.
- SSet.finite_of_monoproof · cited by 3
- CompHausLike.LocallyConstant.presheaf_extproof · cited by 3
- CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.of_monoproof · cited by 2
- CategoryTheory.Presieve.isSheafFor_of_preservesProductproof · cited by 2
- CategoryTheory.Presieve.IsSeparatedFor.of_monoproof · cited by 1
- Condensed.isoFinYonedaComponents_inv_compproof · cited by 1
- LightCondensed.isoFinYonedaComponents_inv_compproof · cited by 1
- CategoryTheory.Presieve.FamilyOfElements.Compatible.of_monoproof · cited by 1
- SSet.relativeCellComplexOfMono.isPullbackproof · cited by 1
- AlgebraicGeometry.Scheme.pullbackComparison_forget_surjectiveproof · cited by 0
- Condensed.isoLocallyConstantOfIsColimit_invproof · cited by 0
- LightCondensed.isoLocallyConstantOfIsColimit_invproof · cited by 0