Theorems · Definition · category theory

CategoryTheory.Localization.HasProductsOfShapeAux.compLimitFunctorIso

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (L : CategoryTheory.Functor C D) →
          (W : CategoryTheory.MorphismProperty C) →
            [inst_2 : L.IsLocalization W] →
              (J : Type) →
                [inst_3 : CategoryTheory.Limits.HasProductsOfShape J C] →
                  [inst_4 : W.IsStableUnderProductsOfShape J] →
                    [inst_5 : W.ContainsIdentities] →
                      [inst_6 : Finite J] →
                        ((CategoryTheory.Functor.whiskeringRight (CategoryTheory.Discrete J) C D).obj L).comp
                            (CategoryTheory.Localization.HasProductsOfShapeAux.limitFunctor L W J) ≅
                          CategoryTheory.Limits.lim.comp L

The functor limitFunctor L W J is induced by lim ⋙ L.

Defined in

Mathlib.CategoryTheory.Localization.FiniteProducts

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Limits.HasProductsOfShapeCategoryTheory.MorphismProperty.IsStableUnderProductsOfShapeCategoryTheory.MorphismProperty.ContainsIdentitiesFinite