Theorems · Definition · category theory

CategoryTheory.GradedObject.mapBifunctorMapObj

{C₁ : Type u_1} →
  {C₂ : Type u_2} →
    {C₃ : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C₁] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} C₃] →
            (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃)) →
              {I : Type u_4} →
                {J : Type u_5} →
                  {K : Type u_6} →
                    (p : I × J → K) →
                      (X : CategoryTheory.GradedObject I C₁) →
                        (Y : CategoryTheory.GradedObject J C₂) →
                          [(((CategoryTheory.GradedObject.mapBifunctor F I J).obj X).obj Y).HasMap p] →
                            CategoryTheory.GradedObject K C₃

Given a bifunctor F : C₁ ⥤ C₂ ⥤ C₃, graded objects X : GradedObject I C₁ and Y : GradedObject J C₂ and a map p : I × J → K, this is the K-graded object sending k to the coproduct of (F.obj (X i)).obj (Y j) for p ⟨i, j⟩ = k.

Defined in

Mathlib.CategoryTheory.GradedObject.Bifunctor

Cited by

64 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.GradedObject.HasMap