Theorems · Theorem · category theory

CategoryTheory.ShrinkHoms.equivalence_counitIso

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C],
  (CategoryTheory.ShrinkHoms.equivalence C).counitIso =
    CategoryTheory.NatIso.ofComponents
      (fun x =>
        CategoryTheory.Iso.refl
          (((CategoryTheory.ShrinkHoms.inverse C).comp (CategoryTheory.ShrinkHoms.functor C)).obj x))
      ⋯

Defined in: Mathlib.CategoryTheory.EssentiallySmall
Cited by: 0 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.LocallySmall

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.Iso.reflstatement · cited by 727
CategoryTheory.Equivalence.counitIsostatement and proof · cited by 480
CategoryTheory.LocallySmallstatement and proof · cited by 242
CategoryTheory.NatIso.ofComponentsstatement · cited by 178
CategoryTheory.ShrinkHomsstatement · cited by 34
CategoryTheory.ShrinkHoms.equivalencestatement and proof · cited by 26

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