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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc

∀ {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) {Z_1 : C} (h : CategoryTheory.MonoidalCategoryStruct.tensorObj W Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W g) h)
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
18 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor · cited by 12MonoidalCategory.whiskerL…CategoryTheory.eHom_whisker_cancel · cited by 2CategoryTheory.eHom_whisk…CategoryTheory.Enriched.FunctorCategory.enriched_assoc · cited by 2FunctorCategory.enriched_…CategoryTheory.Enriched.FunctorCategory.enriched_comp_id · cited by 2FunctorCategory.enriched_…CategoryTheory.eHomWhiskerLeft_comp · cited by 2CategoryTheory.eHomWhiske…CategoryTheory.MonoidalCategory.Limits.pushout.associator_naturality_left_condition · cited by 1pushout.associator_natura…HomologicalComplex.rightUnitor'_inv · cited by 1HomologicalComplex.rightU…CategoryTheory.MonoidalClosed.ihomCurry_ihomUncurry · cited by 1MonoidalClosed.ihomCurry_…CategoryTheory.GradedObject.Monoidal.pentagon_inv · cited by 1Monoidal.pentagon_invCategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ · cited by 1MonoidalCategory.tensorμ_…CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.associator_naturality · cited by 0PushoutProduct.associator…CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forward · cited by 0DayConvolution.hexagon_fo…CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three · cited by 0FunctorCategory.homEquiv_…CategoryTheory.MonObj.Mon_tensor_mul_assoc · cited by 0MonObj.Mon_tensor_mul_ass…CategoryTheory.MonObj.Mon_tensor_mul_one · cited by 0MonObj.Mon_tensor_mul_oneCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategory.whiskerLeft_comp · cited by 82MonoidalCategory.whiskerL…MonoidalCategory.whiskerLeft_…CITED BYCITES

Cites8

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Cited by18

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