Theorems · Theorem · category theory

CategoryTheory.StructuredArrow.preEquivalence_counitIso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C D)
  {G : CategoryTheory.Functor D E} {e : E} (f : CategoryTheory.StructuredArrow e G),
  (CategoryTheory.StructuredArrow.preEquivalence F f).counitIso =
    CategoryTheory.NatIso.ofComponents
      (fun x =>
        CategoryTheory.StructuredArrow.isoMk
          (CategoryTheory.Iso.refl
            (((CategoryTheory.StructuredArrow.preEquivalenceInverse F f).comp
                    (CategoryTheory.StructuredArrow.preEquivalenceFunctor F f)).obj
                x).right)
          ⋯)
      ⋯

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Basic

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category