Theorems · Definition · category theory

CategoryTheory.Limits.pushoutCoconeOfRightIsoIsLimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      (f : X ⟶ Y) →
        (g : X ⟶ Z) →
          [inst_1 : CategoryTheory.IsIso g] →
            CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.pushoutCoconeOfRightIso f g)

Verify that the constructed cocone is indeed a colimit.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso
Cited by: 1 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsIso

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Cites11

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.WalkingPairstatement · cited by 1,319
CategoryTheory.IsIsostatement and proof · cited by 1,156
CategoryTheory.Limits.IsColimitstatement · cited by 773
CategoryTheory.Limits.WalkingSpanstatement · cited by 300
CategoryTheory.Limits.spanstatement · cited by 294
CategoryTheory.Limits.PushoutCoconeproof · cited by 66
CategoryTheory.Limits.PushoutCocone.inlproof · cited by 58
CategoryTheory.Limits.pushoutCoconeOfRightIsostatement and proof · cited by 7
CategoryTheory.Limits.PushoutCocone.isColimitAux'proof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.hasPushout_of_right_isoproof · cited by 2