Theorems · Definition · category theory
CategoryTheory.Limits.MonoFactorisation.I
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → {f : X ⟶ Y} → CategoryTheory.Limits.MonoFactorisation f → CA factorisation of a morphism f = e ≫ m, with m monic.
- Cited by
- 83 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Limits.MonoFactorisationstatement and proof · cited by 69
Cited by114
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.imageproof · cited by 124
- CategoryTheory.Limits.MonoFactorisation.mstatement · cited by 45
- CategoryTheory.Limits.MonoFactorisation.estatement · cited by 39
- CategoryTheory.Limits.image.liftstatement · cited by 16
- CategoryTheory.Limits.IsImage.liftstatement · cited by 15
- CategoryTheory.Limits.MonoFactorisation.facstatement · cited by 13
- CategoryTheory.Limits.image.lift_facstatement · cited by 10
- CategoryTheory.Limits.IsImage.isoExtstatement · cited by 8
- CategoryTheory.Limits.IsImage.lift_facstatement · cited by 8
- CategoryTheory.Limits.MonoFactorisation.copystatement and proof · cited by 6
- CategoryTheory.Limits.MonoFactorisation.ofIsoIstatement and proof · cited by 6
- CategoryTheory.Limits.MonoFactorisation.ofArrowIsoproof · cited by 6