Theorems · Definition · category theory

CategoryTheory.Limits.limitUncurryIsoLimitCompLim

{J : Type u_1} →
  {K : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} J] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} K] →
        {C : Type u_3} →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} C] →
            (F : CategoryTheory.Functor J (CategoryTheory.Functor K C)) →
              [inst_3 : CategoryTheory.Limits.HasLimitsOfShape K C] →
                [inst_4 : CategoryTheory.Limits.HasLimit (CategoryTheory.Functor.uncurry.obj F)] →
                  [inst_5 : CategoryTheory.Limits.HasLimit (F.comp CategoryTheory.Limits.lim)] →
                    CategoryTheory.Limits.limit (CategoryTheory.Functor.uncurry.obj F) ≅
                      CategoryTheory.Limits.limit (F.comp CategoryTheory.Limits.lim)

The Fubini theorem for a functor F : J ⥤ K ⥤ C, showing that the limit of uncurry.obj F can be computed as the limit of the limits of the functors F.obj j.

Defined in

Mathlib.CategoryTheory.Limits.Fubini

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.HasLimitCategoryTheory.Limits.HasLimit