Theorems · Definition · category theory

CategoryTheory.Limits.pushoutRightPushoutInlIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W X Y Z : C} →
      (f : X ⟶ Y) →
        (g : X ⟶ Z) →
          (f' : Y ⟶ W) →
            [inst_1 : CategoryTheory.Limits.HasPushout f g] →
              [inst_2 : CategoryTheory.Limits.HasPushout f' (CategoryTheory.Limits.pushout.inl f g)] →
                CategoryTheory.Limits.pushout f' (CategoryTheory.Limits.pushout.inl f g) ≅
                  CategoryTheory.Limits.pushout (CategoryTheory.CategoryStruct.comp f f') g

The canonical isomorphism W ⨿[Y] (Y ⨿[X] Z) ≅ W ⨿[X] Z

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting

Cited by

10 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutCategoryTheory.Limits.HasPushout