Theorems · Theorem · category theory
CompHausLike.mono_iff_injective
∀ {P : TopCat → Prop} {X Y : CompHausLike P} (f : X ⟶ Y),
CategoryTheory.Mono f ↔ Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.cancel_monoproof · cited by 435
- CategoryTheory.forgetproof · cited by 418
- continuous_constproof · cited by 278
- CompHausLike.toTopstatement and proof · cited by 258
Cited by2
Results whose statement or proof uses this declaration.
- LightCondensed.internallyProjective_free_natUnionInftyproof · cited by 0
- Profinite.exists_lift_of_finite_of_mono_of_epiproof · cited by 0