Theorems · Theorem · category theory

CategoryTheory.tensor_sum

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalPreadditive C] {P Q R S : C} {J : Type u_2}
  (s : Finset J) (f : P ⟶ Q) (g : J → (R ⟶ S)),
  CategoryTheory.MonoidalCategoryStruct.tensorHom f (∑ j ∈ s, g j) =
    ∑ j ∈ s, CategoryTheory.MonoidalCategoryStruct.tensorHom f (g j)

Defined in

Mathlib.CategoryTheory.Monoidal.Preadditive

Cited by

2 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalPreadditive