Theorems · Definition · category theory

CategoryTheory.GradedObject.mapBifunctorMapMapIso

{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) →
                      {X₁ X₂ : CategoryTheory.GradedObject I C₁} →
                        {Y₁ Y₂ : CategoryTheory.GradedObject J C₂} →
                          [inst_3 : (((CategoryTheory.GradedObject.mapBifunctor F I J).obj X₁).obj Y₁).HasMap p] →
                            [inst_4 : (((CategoryTheory.GradedObject.mapBifunctor F I J).obj X₂).obj Y₂).HasMap p] →
                              (X₁ ≅ X₂) →
                                (Y₁ ≅ Y₂) →
                                  (CategoryTheory.GradedObject.mapBifunctorMapObj F p X₁ Y₁ ≅
                                    CategoryTheory.GradedObject.mapBifunctorMapObj F p X₂ Y₂)

The isomorphism mapBifunctorMapObj F p X₁ Y₁ ≅ mapBifunctorMapObj F p X₂ Y₂ induced by isomorphisms X₁ ≅ X₂ and Y₁ ≅ Y₂.

Defined in

Mathlib.CategoryTheory.GradedObject.Bifunctor

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.GradedObject.HasMapCategoryTheory.GradedObject.HasMap