Theorems · Definition · category theory

CategoryTheory.Limits.colimitLimitIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} J] →
        {K : Type u₂} →
          [inst_2 : CategoryTheory.Category.{v₂, u₂} K] →
            [inst_3 : CategoryTheory.Limits.HasLimitsOfShape J C] →
              [inst_4 : CategoryTheory.Limits.HasColimitsOfShape K C] →
                [CategoryTheory.Limits.PreservesLimitsOfShape J CategoryTheory.Limits.colim] →
                  (F : CategoryTheory.Functor J (CategoryTheory.Functor K C)) →
                    CategoryTheory.Limits.colimit (CategoryTheory.Limits.limit F) ≅
                      CategoryTheory.Limits.limit (CategoryTheory.Limits.colimit F.flip)

A curried version of the fact that filtered colimits commute with finite limits.

Defined in

Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit

Cited by

7 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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