Theorems · Theorem · category theory

CategoryTheory.Functor.Final.coconesEquiv_counitIso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [inst_2 : F.Final] {E : Type u₃} [inst_3 : CategoryTheory.Category.{v₃, u₃} E]
  (G : CategoryTheory.Functor D E),
  (CategoryTheory.Functor.Final.coconesEquiv F G).counitIso =
    CategoryTheory.NatIso.ofComponents
      (fun c =>
        CategoryTheory.Limits.Cocone.ext
          (CategoryTheory.Iso.refl
            (((CategoryTheory.Limits.Cocone.whiskering F).comp CategoryTheory.Functor.Final.extendCocone).obj c).pt)
          ⋯)
      ⋯

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.Category