Theorems · Definition · category theory

CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim

{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] →
            (G : CategoryTheory.Functor (J × K) C) →
              [inst_3 : CategoryTheory.Limits.HasLimitsOfShape K C] →
                [inst_4 : CategoryTheory.Limits.HasLimitsOfShape J C] →
                  [inst_5 :
                      CategoryTheory.Limits.HasLimit
                        ((CategoryTheory.Functor.curry.obj G).comp CategoryTheory.Limits.lim)] →
                    CategoryTheory.Limits.limit
                        ((CategoryTheory.Functor.curry.obj ((CategoryTheory.Prod.swap K J).comp G)).comp
                          CategoryTheory.Limits.lim) ≅
                      CategoryTheory.Limits.limit ((CategoryTheory.Functor.curry.obj G).comp CategoryTheory.Limits.lim)

A variant of the Fubini theorem for a functor G : J × K ⥤ C, showing that $\lim_k \lim_j G(j,k) ≅ \lim_j \lim_k G(j,k)$.

Defined in

Mathlib.CategoryTheory.Limits.Fubini

Cited by

2 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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