Theorems · Definition · category theory

CategoryTheory.Limits.coyonedaOpColimitIsoLimitCoyoneda

{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.coyoneda.obj (Opposite.op (CategoryTheory.Limits.colimit F)) ≅
              CategoryTheory.Limits.limit (F.op.comp CategoryTheory.coyoneda)

Hom is functorially cocontinuous: coyoneda of a colimit is the limit over coyoneda of the diagram.

Defined in

Mathlib.CategoryTheory.Limits.IndYoneda

Cited by

5 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit