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Theorems · Definition · category theory

CategoryTheory.Limits.MonoFactorisation.m

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} → {f : X ⟶ Y} → (self : CategoryTheory.Limits.MonoFactorisation f) → self.I ⟶ Y

A factorisation of a morphism f = e ≫ m, with m monic.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Images
Cited by
45 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.Category
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Around this declaration

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CategoryTheory.Limits.image.ι · cited by 104image.ιCategoryTheory.Limits.MonoFactorisation.fac · cited by 13MonoFactorisation.facCategoryTheory.Limits.image.lift_fac · cited by 10image.lift_facCategoryTheory.Limits.IsImage.lift_fac · cited by 8IsImage.lift_facCategoryTheory.Limits.MonoFactorisation.copy · cited by 6MonoFactorisation.copyCategoryTheory.Limits.MonoFactorisation.ofArrowIso · cited by 6MonoFactorisation.ofArrow…CategoryTheory.Limits.MonoFactorisation.ofIsoI · cited by 6MonoFactorisation.ofIsoICategoryTheory.Limits.MonoFactorisation.compMono · cited by 4MonoFactorisation.compMonoCategoryTheory.Limits.MonoFactorisation.ofCompIso · cited by 4MonoFactorisation.ofCompI…CategoryTheory.Limits.IsImage.fac_lift · cited by 4IsImage.fac_liftCategoryTheory.Limits.IsImage.lift_ι · cited by 4IsImage.lift_ιCategoryTheory.Limits.MonoFactorisation.isoComp · cited by 3MonoFactorisation.isoCompCategoryTheory.Limits.MonoFactorisation.ofIsoComp · cited by 3MonoFactorisation.ofIsoCo…CategoryTheory.Limits.IsImage.copy · cited by 2IsImage.copyCategoryTheory.Limits.ImageFactorisation.copy · cited by 2ImageFactorisation.copyCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.MonoFactorisation.I · cited by 83MonoFactorisation.ICategoryTheory.Limits.MonoFactorisation · cited by 69Limits.MonoFactorisationMonoFactorisation.mCITED BYCITES

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Cited by66

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