Theorems · Theorem · category theory

CategoryTheory.Limits.pushout.condition

∀ {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],
  CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.pushout.inl f g) =
    CategoryTheory.CategoryStruct.comp g (CategoryTheory.Limits.pushout.inr f g)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

23 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushout