Theorems · Definition · category theory

CategoryTheory.Ind.limCompInclusion

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {I : Type v} →
      [inst_1 : CategoryTheory.SmallCategory I] →
        [inst_2 : CategoryTheory.IsFiltered I] →
          (CategoryTheory.Ind.lim I).comp (CategoryTheory.Ind.inclusion C) ≅
            ((CategoryTheory.Functor.whiskeringRight I C (CategoryTheory.Functor Cᵒᵖ (Type v))).obj
                  CategoryTheory.yoneda).comp
              CategoryTheory.Limits.colim

Computing ind-lims in Ind C is the same as computing them in Cᵒᵖ ⥤ Type v.

Defined in

Mathlib.CategoryTheory.Limits.Indization.Category

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.SmallCategoryCategoryTheory.IsFiltered