Theorems · Definition · category theory

CategoryTheory.limitCompWhiskeringRightIsoLimitComp

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {E : Type u_3} →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
            {J : Type u_4} →
              [inst_3 : CategoryTheory.Category.{v_4, u_4} J] →
                [inst_4 : CategoryTheory.Limits.HasLimitsOfShape J D] →
                  (F : CategoryTheory.Functor D E) →
                    [inst_5 : CategoryTheory.Limits.PreservesLimitsOfShape J F] →
                      (G : CategoryTheory.Functor J (CategoryTheory.Functor C D)) →
                        CategoryTheory.Limits.limit (G.comp ((CategoryTheory.Functor.whiskeringRight C D E).obj F)) ≅
                          (CategoryTheory.Limits.limit G).comp F

Whiskering right and then taking a limit is the same as taking the limit and applying the functor.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.FunctorCategory

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.PreservesLimitsOfShape