Theorems · Definition · category theory

CategoryTheory.Functor.Final.coconesEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          [F.Final] →
            {E : Type u₃} →
              [inst_3 : CategoryTheory.Category.{v₃, u₃} E] →
                (G : CategoryTheory.Functor D E) →
                  CategoryTheory.Limits.Cocone (F.comp G) ≌ CategoryTheory.Limits.Cocone G

If F is final, the category of cocones on F ⋙ G is equivalent to the category of cocones on G, for any G : D ⥤ E.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.Category