Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X Y : C),
  CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.MonoidalCategoryStruct.rightUnitor Y).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.associator X Y (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).inv
      (CategoryTheory.MonoidalCategoryStruct.rightUnitor (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)).hom
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
12 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.whiskerLeft_rightUnitor_inv · cited by 8MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.tensor_right_unitality · cited by 3MonoidalCategory.tensor_r…Bimod.TensorBimod.actRight_one' · cited by 3TensorBimod.actRight_one'CategoryTheory.HopfObj.mul_antipode₂ · cited by 1HopfObj.mul_antipode₂CategoryTheory.braiding_rightUnitor_aux₂ · cited by 1CategoryTheory.braiding_r…CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_assoc · cited by 1MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.rightUnitor_tensor_hom · cited by 1MonoidalCategory.rightUni…CategoryTheory.HopfObj.antipode_comul₂ · cited by 1HopfObj.antipode_comul₂CategoryTheory.braiding_rightUnitor_aux₁ · cited by 0CategoryTheory.braiding_r…CategoryTheory.FreeMonoidalCategory.normalize_naturality · cited by 0FreeMonoidalCategory.norm…CategoryTheory.tensorRightHomEquiv_tensor · cited by 0CategoryTheory.tensorRigh…Bimod.whiskerRight_id_bimod · cited by 0Bimod.whiskerRight_id_bim…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.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.whiskerRight · cited by 903MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.associator · cited by 667MonoidalCategoryStruct.as…CategoryTheory.MonoidalCategoryStruct.leftUnitor · cited by 437MonoidalCategoryStruct.le…CategoryTheory.MonoidalCategoryStruct.rightUnitor · cited by 397MonoidalCategoryStruct.ri…CategoryTheory.cancel_epi · cited by 380CategoryTheory.cancel_epiCategoryTheory.MonoidalCategory.comp_whiskerRight · cited by 76MonoidalCategory.comp_whi…MonoidalCategory.whiskerLeft_…CITED BYCITES

Cites21

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

Cited by12

Results whose statement or proof uses this declaration.