Theorems · Definition · category theory

CategoryTheory.Functor.PushoutObjObj.inl

{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} → (self : F.PushoutObjObj f₁ f₂) → (F.obj Y₁).obj X₂ ⟶ self.pt

the first inclusion

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

31 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category