Theorems · Theorem · category theory

CategoryTheory.AddMonObj.AddMon_tensor_zero_add

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (M N : C) [inst_3 : CategoryTheory.AddMonObj M]
  [inst_4 : CategoryTheory.AddMonObj N],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).inv
          (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.AddMonObj.zero CategoryTheory.AddMonObj.zero))
        (CategoryTheory.MonoidalCategoryStruct.tensorObj M N))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.tensorμ M N M N)
        (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.AddMonObj.add CategoryTheory.AddMonObj.add)) =
    (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorObj M N)).hom

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.AddMonObjCategoryTheory.AddMonObj