Theorems · Theorem · category theory

CategoryTheory.GradedObject.Monoidal.braiding_naturality_right

∀ {I : Type u_1} [inst : AddCommMonoid I] {C : Type u_2} [inst_1 : CategoryTheory.Category.{v_1, u_2} C]
  [inst_2 : CategoryTheory.MonoidalCategory C] (X : CategoryTheory.GradedObject I C)
  {Y Z : CategoryTheory.GradedObject I C} [inst_3 : CategoryTheory.BraidedCategory C] [inst_4 : X.HasTensor Y]
  [inst_5 : Y.HasTensor X] [inst_6 : X.HasTensor Z] [inst_7 : Z.HasTensor X] (f : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.GradedObject.Monoidal.whiskerLeft X f)
      (CategoryTheory.GradedObject.Monoidal.braiding X Z).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.GradedObject.Monoidal.braiding X Y).hom
      (CategoryTheory.GradedObject.Monoidal.whiskerRight f X)

Defined in

Mathlib.CategoryTheory.GradedObject.Braiding

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensor