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Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.leftUnitorNatIso

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      CategoryTheory.MonoidalCategory.tensorUnitLeft C ≅ CategoryTheory.Functor.id C

The left unitor as a natural isomorphism.

Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
5 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.GradedObject.Monoidal.leftUnitor · cited by 4Monoidal.leftUnitorCategoryTheory.Functor.OplaxMonoidal.ofBifunctor.leftMapₗ · cited by 1ofBifunctor.leftMapₗCategoryTheory.Functor.LaxMonoidal.ofBifunctor.bottomMapₗ · cited by 1ofBifunctor.bottomMapₗCategoryTheory.GradedObject.Monoidal.leftUnitor_naturality · cited by 1Monoidal.leftUnitor_natur…CategoryTheory.Functor.OplaxMonoidal.ofBifunctor.topMapₗ · cited by 1ofBifunctor.topMapₗCategoryTheory.Functor.LaxMonoidal.ofBifunctor.leftMapₗ · cited by 1ofBifunctor.leftMapₗCategoryTheory.Localization.Monoidal.leftUnitor · cited by 1Monoidal.leftUnitorCategoryTheory.Localization.Monoidal.leftUnitor_hom_app · cited by 1Monoidal.leftUnitor_hom_a…CategoryTheory.unitClosed · cited by 0CategoryTheory.unitClosedCategoryTheory.GradedObject.Monoidal.triangle · cited by 0Monoidal.triangleCategoryTheory.MonoidalClosed.unitNatIso · cited by 0MonoidalClosed.unitNatIsoCategoryTheory.MonoidalCategory.leftUnitorNatIso_hom_app · cited by 0MonoidalCategory.leftUnit…CategoryTheory.MonoidalCategory.leftUnitorNatIso_inv_app · cited by 0MonoidalCategory.leftUnit…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.leftUnitor · cited by 437MonoidalCategoryStruct.le…CategoryTheory.NatIso.ofComponents · cited by 178NatIso.ofComponentsCategoryTheory.MonoidalCategory.tensorUnitLeft · cited by 8MonoidalCategory.tensorUn…MonoidalCategory.leftUnitorNa…CITED BYCITES

Cites8

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Cited by13

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