Theorems · Definition · category theory

CategoryTheory.Limits.pushoutCoconeOfRightIso

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

If f : X ⟶ Z is iso, then Y ⨿[X] Z ≅ Y. This is the explicit colimit cocone.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso
Cited by: 7 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsIso

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

Cites8

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.compproof · cited by 17,999
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.IsIsostatement and proof · cited by 1,156
CategoryTheory.invproof · cited by 467
CategoryTheory.Limits.PushoutCocone.mkproof · cited by 89
CategoryTheory.Limits.PushoutCoconestatement · cited by 66

Cited by8

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.hasPushout_of_right_isoproof · cited by 2
CategoryTheory.Limits.pushoutCoconeOfRightIsoIsLimitstatement and proof · cited by 1
CategoryTheory.Limits.pushoutCoconeOfRightIso_inlstatement · cited by 0
CategoryTheory.Limits.pushoutCoconeOfRightIso_inrstatement · cited by 0
CategoryTheory.Limits.pushoutCoconeOfRightIso_xstatement · cited by 0
CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_leftstatement · cited by 0
CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_nonestatement and proof · cited by 0
CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_rightstatement · cited by 0