Theorems · Theorem · category theory
CategoryTheory.ofHom_mono_iff_injective
∀ {X Y : Type u} (f : X → Y), CategoryTheory.Mono (TypeCat.ofHom f) ↔ Function.Injective fA morphism in Type is a monomorphism if and only if it is injective.
- Defined in
- Mathlib.CategoryTheory.Types.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, 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.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.cancel_monoproof · cited by 435
- TypeCat.ofHomstatement and proof · cited by 389
- CategoryTheory.ConcreteCategory.congr_homproof · cited by 138
- CategoryTheory.ConcreteCategory.hom_extproof · cited by 48
- Function.Injective.comp_leftproof · cited by 15
- CategoryTheory.homOfElement_eq_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CompHausLike.mono_iff_injectiveproof · cited by 2
- CategoryTheory.ShortComplex.SnakeInput.δ_apply'proof · cited by 1