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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.whiskerRight_id

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X Y : C}
  (f : X ⟶ Y),
  CategoryTheory.MonoidalCategoryStruct.whiskerRight f (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).hom
      (CategoryTheory.CategoryStruct.comp f (CategoryTheory.MonoidalCategoryStruct.rightUnitor Y).inv)
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
38 results in Mathlib
Foundations
Depth 5 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst · cited by 13CartesianMonoidalCategory…CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality · cited by 4MonoidalCategory.rightUni…CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app · cited by 4DayConvolutionUnit.rightU…CategoryTheory.MonoidalCategory.whiskerRight_id_assoc · cited by 4MonoidalCategory.whiskerR…CategoryTheory.MonObj.ext · cited by 3MonObj.extCategoryTheory.MonoidalCategory.tensor_left_unitality · cited by 3MonoidalCategory.tensor_l…CategoryTheory.MonoidalCategory.tensor_right_unitality · cited by 3MonoidalCategory.tensor_r…Bimod.TensorBimod.actRight_one' · cited by 3TensorBimod.actRight_one'CategoryTheory.AddMonObj.ext · cited by 3AddMonObj.extCategoryTheory.HopfObj.one_antipode · cited by 2HopfObj.one_antipodeCategoryTheory.Enriched.FunctorCategory.enriched_comp_id · cited by 2FunctorCategory.enriched_…CategoryTheory.Iso.eHomCongr_comp · cited by 2Iso.eHomCongr_compCategoryTheory.MonoidalCategory.whiskerRight_iff · cited by 2MonoidalCategory.whiskerR…CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ · cited by 1LaxMonoidal.tensorHom_ε_c…CategoryTheory.Functor.OplaxMonoidal.δ_comp_tensorHom_η · cited by 1OplaxMonoidal.δ_comp_tens…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.Category.assoc · cited by 6433Category.assocCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategoryStruct.whiskerRight · cited by 903MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.rightUnitor · cited by 397MonoidalCategoryStruct.ri…CategoryTheory.Iso.hom_inv_id · cited by 264Iso.hom_inv_idCategoryTheory.MonoidalCategory.rightUnitor_naturality · cited by 7MonoidalCategory.rightUni…MonoidalCategory.whiskerRight…CITED BYCITES

Cites14

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Cited by38

Results whose statement or proof uses this declaration.