Theorems · Definition · category theory

CategoryTheory.GradedObject.mapBifunctorRightUnitor

{C : Type u_1} →
  {D : Type u_2} →
    {I : Type u_3} →
      {J : Type u_4} →
        [inst : CategoryTheory.Category.{v_1, u_1} C] →
          [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
            [inst_2 : Zero I] →
              [inst_3 : DecidableEq I] →
                [inst_4 : CategoryTheory.Limits.HasInitial C] →
                  (F : CategoryTheory.Functor D (CategoryTheory.Functor C D)) →
                    (Y : C) →
                      (F.flip.obj Y ≅ CategoryTheory.Functor.id D) →
                        [∀ (X : D), CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C) (F.obj X)] →
                          (p : J × I → J) →
                            (∀ (j : J), p (j, 0) = j) →
                              (X : CategoryTheory.GradedObject J D) →
                                [inst_6 :
                                    (((CategoryTheory.GradedObject.mapBifunctor F J I).obj X).obj
                                          ((CategoryTheory.GradedObject.single₀ I).obj Y)).HasMap
                                      p] →
                                  CategoryTheory.GradedObject.mapBifunctorMapObj F p X
                                      ((CategoryTheory.GradedObject.single₀ I).obj Y) ≅
                                    X

Given F : D ⥤ C ⥤ D, Y : C, e : F.flip.obj Y ≅ 𝟭 D, X : GradedObject J D and p : J × I → J such that p ⟨j, 0⟩ = j for all j, this is the right unitor isomorphism mapBifunctorMapObj F p X ((single₀ I).obj Y) ≅ X.

Defined in

Mathlib.CategoryTheory.GradedObject.Unitor

Cited by

10 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryZeroDecidableEqCategoryTheory.Limits.HasInitialCategoryTheory.Limits.PreservesColimitCategoryTheory.GradedObject.HasMap