Theorems · Inductive type · category theory

CategoryTheory.Functor.PushoutObjObj

{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] →
            CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃) →
              {X₁ Y₁ : C₁} → (X₁ ⟶ Y₁) → {X₂ Y₂ : C₂} → (X₂ ⟶ Y₂) → Type (max u₃ v₃)

Given a bifunctor F : C₁ ⥤ C₂ ⥤ C₃, and morphisms f₁ : X₁ ⟶ Y₁ in C₁ and f₂ : X₂ ⟶ Y₂ in C₂, this structure contains the data of a pushout of (F.obj Y₁).obj X₂ and (F.obj X₁).obj Y₂ along (F.obj X₁).obj X₂.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

54 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category