Theorems · Inductive type · category theory
CategoryTheory.Limits.MonoFactorisation
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → (X ⟶ Y) → Type (max u v)A factorisation of a morphism f = e ≫ m, with m monic.
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
Cited by129
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.MonoFactorisation.Istatement and proof · cited by 83
- CategoryTheory.Limits.MonoFactorisation.mstatement and proof · cited by 45
- CategoryTheory.Limits.MonoFactorisation.estatement and proof · cited by 39
- CategoryTheory.Limits.IsImagestatement · cited by 26
- CategoryTheory.Limits.StrongEpiMonoFactorisation.toMonoFactorisationstatement · cited by 18
- CategoryTheory.Limits.image.liftstatement and proof · cited by 16
- CategoryTheory.Limits.IsImage.liftstatement and proof · cited by 15
- CategoryTheory.Limits.Image.monoFactorisationstatement · cited by 15
- CategoryTheory.Limits.MonoFactorisation.facstatement and proof · cited by 13
- CategoryTheory.Limits.image.lift_facstatement and proof · cited by 10
- CategoryTheory.Limits.ImageFactorisation.Fstatement · cited by 9
- CategoryTheory.Limits.StrongEpiMonoFactorisation.toMonoIsImageproof · cited by 9