Theorems · Definition · category theory

CategoryTheory.Join.mapPairComp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {E : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            {E' : Type u₄} →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} E'] →
                {J : Type u₅} →
                  [inst_4 : CategoryTheory.Category.{v₅, u₅} J] →
                    {K : Type u₆} →
                      [inst_5 : CategoryTheory.Category.{v₆, u₆} K] →
                        (Fₗ : CategoryTheory.Functor C E) →
                          (Fᵣ : CategoryTheory.Functor D E') →
                            (Gₗ : CategoryTheory.Functor E J) →
                              (Gᵣ : CategoryTheory.Functor E' K) →
                                CategoryTheory.Join.mapPair (Fₗ.comp Gₗ) (Fᵣ.comp Gᵣ) ≅
                                  (CategoryTheory.Join.mapPair Fₗ Fᵣ).comp (CategoryTheory.Join.mapPair Gₗ Gᵣ)

mapPair respects composition

Defined in

Mathlib.CategoryTheory.Join.Basic

Cited by

20 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category