Theorems · Theorem · category theory
CategoryTheory.Limits.MonoFactorisation.fac
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y}
(self : CategoryTheory.Limits.MonoFactorisation f), CategoryTheory.CategoryStruct.comp self.e self.m = fA factorisation of a morphism f = e ≫ m, with m monic.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Limits.MonoFactorisation.Istatement · cited by 83
- CategoryTheory.Limits.MonoFactorisationstatement and proof · cited by 69
- CategoryTheory.Limits.MonoFactorisation.mstatement · cited by 45
- CategoryTheory.Limits.MonoFactorisation.estatement · cited by 39
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.image.facproof · cited by 27
- CategoryTheory.Limits.IsImage.fac_liftproof · cited by 4
- ModuleCat.image.lift_facproof · cited by 0
- CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.isNormalEpiCategoryproof · cited by 0
- CategoryTheory.Limits.Types.Image.lift_facproof · cited by 0
- AddCommGrpCat.image.lift_facproof · cited by 0
- CategoryTheory.Regular.frobeniusMorphism_isPullbackproof · cited by 0
- CategoryTheory.Limits.MonoFactorisation.fac_applyproof · cited by 0
- CategoryTheory.Limits.MonoFactorisation.fac_assocproof · cited by 0
- CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisationproof · cited by 0