Theorems · Definition · category theory

CategoryTheory.MonoidalClosed.unitNatIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.Closed (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)] →
        CategoryTheory.Functor.id C ≅ CategoryTheory.ihom (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)

The internal hom out of the unit is naturally isomorphic to the identity functor.

Defined in: Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.Closed

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
CategoryTheory.ihomstatement · cited by 179
CategoryTheory.Closedstatement and proof · cited by 90
CategoryTheory.ihom.adjunctionproof · cited by 31
CategoryTheory.Adjunction.idproof · cited by 12
CategoryTheory.MonoidalCategory.leftUnitorNatIsoproof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalClosed.unitIsoSelfproof · cited by 0