Theorems · Definition · category theory

CategoryTheory.Limits.PreservesPushout.iso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {W X Y : C} →
            (f : W ⟶ X) →
              (g : W ⟶ Y) →
                [CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.span f g) G] →
                  [inst_3 : CategoryTheory.Limits.HasPushout f g] →
                    [inst_4 : CategoryTheory.Limits.HasPushout (G.map f) (G.map g)] →
                      CategoryTheory.Limits.pushout (G.map f) (G.map g) ≅ G.obj (CategoryTheory.Limits.pushout f g)

If G preserves the pushout of (f,g), then the pushout comparison map for G at (f,g) is an isomorphism.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks

Cited by

11 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.HasPushoutCategoryTheory.Limits.HasPushout