Theorems · Definition · category theory

CategoryTheory.Functor.leibnizPushout

{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) →
              [CategoryTheory.Limits.HasPushouts C₃] →
                CategoryTheory.Functor (CategoryTheory.Arrow C₁)
                  (CategoryTheory.Functor (CategoryTheory.Arrow C₂) (CategoryTheory.Arrow C₃))

Given a bifunctor F : C₁ ⥤ C₂ ⥤ C₃ to a category C₃ which has pushouts, the Leibniz pushout (pushout-product) of f₁ : X₁ ⟶ Y₁ in C₁ and f₂ : X₂ ⟶ Y₂ in C₂ is the map pushout ((F.map f₁).app X₂) ((F.obj X₁).map f₂) ⟶ (F.obj Y₁).obj Y₂ induced by the diagram `` (F.obj X₁).obj X₂ -> (F.obj Y₁).obj X₂ | | | | v v (F.obj X₁).obj Y₂ -> (F.obj Y₁).obj Y₂ ``

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

8 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPushouts