Theorems · Definition · category theory

CategoryTheory.Limits.colimitLimitToLimitColimitCone

{J : Type u₁} →
  {K : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} J] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} K] →
        {C : Type u} →
          [inst_2 : CategoryTheory.Category.{v, u} C] →
            [inst_3 : CategoryTheory.Limits.HasLimitsOfShape J C] →
              [inst_4 : CategoryTheory.Limits.HasColimitsOfShape K C] →
                (G : CategoryTheory.Functor J (CategoryTheory.Functor K C)) →
                  [inst_5 : CategoryTheory.Limits.HasLimit G] →
                    CategoryTheory.Limits.colim.mapCone (CategoryTheory.Limits.limit.cone G) ⟶
                      CategoryTheory.Limits.limit.cone (G.comp CategoryTheory.Limits.colim)

The map colimit_limit_to_limit_colimit realized as a map of cones.

Defined in

Mathlib.CategoryTheory.Limits.ColimitLimit

Cited by

1 results in Mathlib

Foundations

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

Assumes

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