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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X Y : C),
  CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).inv Y =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)).inv
      (CategoryTheory.MonoidalCategoryStruct.associator (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X Y).inv
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
7 results in Mathlib
Foundations
Depth 21 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.MonoidalCategory.leftUnitor_tensor_inv · cited by 3MonoidalCategory.leftUnit…CategoryTheory.MonoidalCategory.tensor_left_unitality · cited by 3MonoidalCategory.tensor_l…CategoryTheory.MonoidalCategory.leftUnitor_monoidal · cited by 3MonoidalCategory.leftUnit…CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv' · cited by 1MonoidalCategory.leftUnit…CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id · cited by 1MonoidalCategory.leftUnit…CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight_assoc · cited by 1MonoidalCategory.leftUnit…CategoryTheory.eComp_eHomWhiskerRight · cited by 1CategoryTheory.eComp_eHom…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.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.associator · cited by 667MonoidalCategoryStruct.as…CategoryTheory.MonoidalCategoryStruct.leftUnitor · cited by 437MonoidalCategoryStruct.le…CategoryTheory.IsIso.Iso.inv_inv · cited by 30Iso.inv_invCategoryTheory.IsIso.inv_comp · cited by 22IsIso.inv_compCategoryTheory.eq_of_inv_eq_inv · cited by 19CategoryTheory.eq_of_inv_…CategoryTheory.MonoidalCategory.inv_whiskerRight · cited by 10MonoidalCategory.inv_whis…MonoidalCategory.leftUnitor_i…CITED BYCITES

Cites16

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Cited by7

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