Theorems · Definition · category theory

CategoryTheory.Limits.colimitHomIsoLimitYoneda

{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    {I : Type v₁} →
      [inst_1 : CategoryTheory.Category.{v₂, v₁} I] →
        (F : CategoryTheory.Functor I C) →
          [inst_2 : CategoryTheory.Limits.HasColimit F] →
            [CategoryTheory.Limits.HasLimitsOfShape Iᵒᵖ (Type u₂)] →
              (A : C) →
                (CategoryTheory.Limits.colimit F ⟶ A) ≅
                  CategoryTheory.Limits.limit (F.op.comp (CategoryTheory.yoneda.obj A))

Hom is cocontinuous: homomorphisms from a colimit is the limit over yoneda of the diagram.

Defined in

Mathlib.CategoryTheory.Limits.IndYoneda

Cited by

7 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitCategoryTheory.Limits.HasLimitsOfShape