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Theorems · Definition · category theory

CategoryTheory.Limits.MonoFactorisation.ofIsoI

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

Given a mono factorisation X ⟶ I ⟶ Y of an arrow f, an isomorphism I ≅ I' gives a new mono factorisation X ⟶ I' ⟶ Y of f.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Images
Cited by
6 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Limits.IsImage.ofIsoI · cited by 2IsImage.ofIsoICategoryTheory.Limits.ImageFactorisation.ofIsoI · cited by 2ImageFactorisation.ofIsoICategoryTheory.Limits.MonoFactorisation.ofIsoI_I · cited by 0MonoFactorisation.ofIsoI_ICategoryTheory.Limits.MonoFactorisation.ofIsoI_e · cited by 0MonoFactorisation.ofIsoI_eCategoryTheory.Limits.MonoFactorisation.ofIsoI_m · cited by 0MonoFactorisation.ofIsoI_mCategoryTheory.Limits.IsImage.ofIsoI_lift · cited by 0IsImage.ofIsoI_liftCategoryTheory.Limits.ImageFactorisation.ofIsoI_F · cited by 0ImageFactorisation.ofIsoI…CategoryTheory.Limits.ImageFactorisation.ofIsoI_isImage · cited by 0ImageFactorisation.ofIsoI…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.MonoFactorisation.I · cited by 83MonoFactorisation.ICategoryTheory.Limits.MonoFactorisation · cited by 69Limits.MonoFactorisationCategoryTheory.Limits.MonoFactorisation.m · cited by 45MonoFactorisation.mCategoryTheory.Limits.MonoFactorisation.e · cited by 39MonoFactorisation.eMonoFactorisation.ofIsoICITED BYCITES

Cites10

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Cited by8

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