Theorems · Theorem · category theory

CategoryTheory.Limits.pushout.hom_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z}
  [inst_1 : CategoryTheory.Limits.HasPushout f g] {W : C} {k l : CategoryTheory.Limits.pushout f g ⟶ W},
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inl f g) k =
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inl f g) l →
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inr f g) k =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inr f g) l →
      k = l

Two morphisms out of a pushout are equal if their compositions with the pushout morphisms are equal

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

30 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushout