Theorems · Theorem · category theory
CategoryTheory.Functor.mono_of_mono_map
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) [F.ReflectsMonomorphisms] {X Y : C} {f : Y ⟶ X},
CategoryTheory.Mono (F.map f) → CategoryTheory.Mono f- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Functor.ReflectsMonomorphismsstatement and proof · cited by 11
- CategoryTheory.Functor.ReflectsMonomorphisms.reflectsproof · cited by 1
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.ConcreteCategory.mono_of_injectiveproof · cited by 12
- TopCat.mono_iff_injectiveproof · cited by 8
- Rep.mono_iff_injectiveproof · cited by 6
- CategoryTheory.Preadditive.mono_iff_injectiveproof · cited by 3
- CategoryTheory.Functor.mono_map_iff_monoproof · cited by 3
- CompHausLike.mono_iff_injectiveproof · cited by 2
- CategoryTheory.Functor.ReflectsMonomorphisms.of_isoproof · cited by 2
- CategoryTheory.StructuredArrow.mono_of_mono_rightproof · cited by 1
- CategoryTheory.ConcreteCategory.injective_le_monomorphismsproof · cited by 1
- CategoryTheory.Sheaf.Hom.mono_of_presheaf_monoproof · cited by 1
- CategoryTheory.Sheaf.mono_of_injectiveproof · cited by 1
- CategoryTheory.Endofunctor.Coalgebra.mono_of_monoproof · cited by 0