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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.whiskerLeft_id

∀ {C : Type u} {𝒞 : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.MonoidalCategory C] (X Y : C),
  CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.CategoryStruct.id Y) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
52 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.MonoidalCategory.tensorHom_id · cited by 67MonoidalCategory.tensorHo…CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fst · cited by 6CartesianMonoidalCategory…CategoryTheory.MonoidalClosed.uncurry_id_eq_ev · cited by 6MonoidalClosed.uncurry_id…CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ · cited by 4Monoidal.whiskerLeft_μ_δCategoryTheory.MonoidalCategory.whiskerLeft_eqToHom · cited by 4MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app · cited by 4DayConvolutionUnit.leftUn…CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom · cited by 4MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app · cited by 4DayConvolutionUnit.rightU…CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit · cited by 4DayConvolution.associator…CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_hom · cited by 3MonTauto.mul_assoc_homCategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_hom · cited by 3MonTauto.add_assoc_homAction.rightUnitor_hom_hom · cited by 2Action.rightUnitor_hom_homCategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_app · cited by 2DayConvolution.whiskerRig…CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv · cited by 2MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv' · cited by 2MonoidalCategory.whiskerL…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…MonoidalCategory.whiskerLeft_…CITED BYCITES

Cites6

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Cited by52

Results whose statement or proof uses this declaration.