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Theorems · Definition · category theory

CategoryTheory.MonoidalCategoryStruct.leftUnitor

{C : Type u} →
  {𝒞 : CategoryTheory.Category.{v, u} C} →
    [self : CategoryTheory.MonoidalCategoryStruct C] →
      (X : C) →
        CategoryTheory.MonoidalCategoryStruct.tensorObj (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X ≅ X

The left unitor: 𝟙_ C ⊗ X ≃ X

Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
437 results in Mathlib
Foundations
Depth 3 from the axioms, rests on 6 definitions · uses no axioms
Assumes
CategoryTheory.MonoidalCategoryStruct

Around this declaration

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

CategoryTheory.MonoidalCategory.id_whiskerLeft · cited by 29MonoidalCategory.id_whisk…CategoryTheory.eHomWhiskerRight · cited by 25CategoryTheory.eHomWhiske…CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd · cited by 19CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd · cited by 16CartesianMonoidalCategory…CategoryTheory.leftAdjointMate · cited by 13CategoryTheory.leftAdjoin…CategoryTheory.rightAdjointMate · cited by 13CategoryTheory.rightAdjoi…CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor · cited by 12MonoidalCategory.whiskerL…CategoryTheory.MonObj.one_mul · cited by 10MonObj.one_mulCategoryTheory.SemiCartesianMonoidalCategory.snd_def · cited by 10SemiCartesianMonoidalCate…CategoryTheory.tensorLeftHomEquiv · cited by 9CategoryTheory.tensorLeft…AugmentedSimplexCategory.inr · cited by 9AugmentedSimplexCategory.…CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight · cited by 9MonoidalCategory.leftUnit…CategoryTheory.MonoidalCategory.triangle · cited by 8MonoidalCategory.triangleCategoryTheory.Monoidal.transportStruct · cited by 8Monoidal.transportStructCategoryTheory.Functor.OplaxMonoidal.δ_snd · cited by 7OplaxMonoidal.δ_sndCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategoryStruct · cited by 26CategoryTheory.MonoidalCa…MonoidalCategoryStruct.leftUn…CITED BYCITES

Cites5

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Cited by540

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