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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.whiskerLeft_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (W : C)
  {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z),
  CategoryTheory.MonoidalCategoryStruct.whiskerLeft W (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W f)
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W g)
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
82 results in Mathlib
Foundations
Depth 7 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc · cited by 18MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight · cited by 9MonoidalCategory.leftUnit…Bimod.AssociatorBimod.hom_left_act_hom' · cited by 5AssociatorBimod.hom_left_…Bimod.AssociatorBimod.hom_right_act_hom' · cited by 5AssociatorBimod.hom_right…CategoryTheory.MonoidalCategory.associator_inv_naturality · cited by 4MonoidalCategory.associat…CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δ · cited by 4Monoidal.whiskerLeft_μ_δCategoryTheory.MonoidalCategory.id_tensor_comp · cited by 4MonoidalCategory.id_tenso…CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom · cited by 4MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.tensor_left_unitality · cited by 3MonoidalCategory.tensor_l…CategoryTheory.MonoidalCategory.tensor_right_unitality · cited by 3MonoidalCategory.tensor_r…CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_neg · cited by 3MonTauto.add_assoc_negCategoryTheory.MonoidalCategory.leftUnitor_monoidal · cited by 3MonoidalCategory.leftUnit…CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv · cited by 3MonTauto.mul_assoc_invBimod.TensorBimod.actRight_one' · cited by 3TensorBimod.actRight_one'Bimod.TensorBimod.left_assoc' · cited by 3TensorBimod.left_assoc'CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.MonoidalCategoryStruct.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.tensorHom · cited by 587MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom · cited by 31MonoidalCategory.tensorHo…MonoidalCategory.whiskerLeft_…CITED BYCITES

Cites10

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Cited by82

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