Theorems · Theorem · category theory

CategoryTheory.AddMonObj.add_add_add_comm

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] (M : C)
  [inst_2 : CategoryTheory.AddMonObj M] [inst_3 : CategoryTheory.BraidedCategory C] [CategoryTheory.IsCommAddMonObj M],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.tensorμ M M M M)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.AddMonObj.add CategoryTheory.AddMonObj.add)
        CategoryTheory.AddMonObj.add) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.AddMonObj.add CategoryTheory.AddMonObj.add)
      CategoryTheory.AddMonObj.add

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

1 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.AddMonObjCategoryTheory.BraidedCategoryCategoryTheory.IsCommAddMonObj