Theorems · Theorem · category theory

CategoryTheory.Functor.PushoutObjObj.hom_ext

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  {F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃)} {X₁ Y₁ : C₁} {f₁ : X₁ ⟶ Y₁} {X₂ Y₂ : C₂} {f₂ : X₂ ⟶ Y₂}
  (sq : F.PushoutObjObj f₁ f₂) {X₃ : C₃} {f g : sq.pt ⟶ X₃},
  CategoryTheory.CategoryStruct.comp sq.inl f = CategoryTheory.CategoryStruct.comp sq.inl g →
    CategoryTheory.CategoryStruct.comp sq.inr f = CategoryTheory.CategoryStruct.comp sq.inr g → f = g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

5 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category