Theorems · Definition · category theory

CategoryTheory.Limits.colimitCompWhiskeringLeftIsoCompColimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u'} →
      [inst_1 : CategoryTheory.Category.{v', u'} D] →
        {J : Type u₁} →
          [inst_2 : CategoryTheory.Category.{v₁, u₁} J] →
            {K : Type u₂} →
              [inst_3 : CategoryTheory.Category.{v₂, u₂} K] →
                (F : CategoryTheory.Functor J (CategoryTheory.Functor K C)) →
                  (G : CategoryTheory.Functor D K) →
                    [inst_4 : CategoryTheory.Limits.HasColimitsOfShape J C] →
                      CategoryTheory.Limits.colimit (F.comp ((CategoryTheory.Functor.whiskeringLeft D K C).obj G)) ≅
                        G.comp (CategoryTheory.Limits.colimit F)

Taking a colimit after whiskering by G is the same as using G and then taking a colimit.

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Basic

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShape