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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.rightUnitor_naturality

∀ {C : Type u} {𝒞 : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.MonoidalCategory C] {X Y : C} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight f (CategoryTheory.MonoidalCategoryStruct.tensorUnit C))
      (CategoryTheory.MonoidalCategoryStruct.rightUnitor Y).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).hom f

Naturality of the right unitor: commutativity of X ⊗ 𝟙_ C ⟶ Y ⊗ 𝟙_ C ⟶ Y and X ⊗ 𝟙_ C ⟶ X ⟶ Y

Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
7 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.MonoidalCategory
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CategoryTheory.MonoidalCategory.whiskerRight_id · cited by 38MonoidalCategory.whiskerR…CategoryTheory.HopfObj.mul_antipode₂ · cited by 1HopfObj.mul_antipode₂CategoryTheory.AddMonObj.add_zero_hom · cited by 1AddMonObj.add_zero_homCategoryTheory.MonObj.mul_one_hom · cited by 1MonObj.mul_one_homCategoryTheory.MonoidalCategory.rightUnitor_naturality_assoc · cited by 0MonoidalCategory.rightUni…CategoryTheory.AddMonObj.add_rightUnitor · cited by 0AddMonObj.add_rightUnitorCategoryTheory.MonObj.mul_rightUnitor · cited by 0MonObj.mul_rightUnitorCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategoryStruct.whiskerRight · cited by 903MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.rightUnitor · cited by 397MonoidalCategoryStruct.ri…MonoidalCategory.rightUnitor_…CITED BYCITES

Cites9

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Cited by7

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