Theorems · Definition · category theory

CategoryTheory.Limits.colimitIsoColimitCurryCompColim

{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.HasColimitsOfShape K C] →
                [inst_4 :
                    CategoryTheory.Limits.HasColimit
                      ((CategoryTheory.Functor.curry.obj G).comp CategoryTheory.Limits.colim)] →
                  CategoryTheory.Limits.colimit G ≅
                    CategoryTheory.Limits.colimit
                      ((CategoryTheory.Functor.curry.obj G).comp CategoryTheory.Limits.colim)

The Fubini theorem for a functor G : J × K ⥤ C, showing that the colimit of G can be computed as the colimit of the colimits of the functors G.obj (j, _).

Defined in

Mathlib.CategoryTheory.Limits.Fubini

Cited by

6 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimit