Theorems · Theorem · category theory

CategoryTheory.leftDistributor_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.MonoidalCategory C] [inst_3 : CategoryTheory.MonoidalPreadditive C]
  [inst_4 : CategoryTheory.Limits.HasFiniteBiproducts C] {J : Type} [inst_5 : Finite J] (X Y : C) (f : J → C),
  (CategoryTheory.MonoidalCategory.tensorIso (CategoryTheory.asIso (CategoryTheory.CategoryStruct.id X))
        (CategoryTheory.leftDistributor Y f) ≪≫
      CategoryTheory.leftDistributor X fun j => CategoryTheory.MonoidalCategoryStruct.tensorObj Y (f j)) =
    (CategoryTheory.MonoidalCategoryStruct.associator X Y (⨁ f)).symm ≪≫
      CategoryTheory.leftDistributor (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) f ≪≫
        CategoryTheory.Limits.biproduct.mapIso fun x => CategoryTheory.MonoidalCategoryStruct.associator X Y (f x)

Defined in

Mathlib.CategoryTheory.Monoidal.Preadditive

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalPreadditiveCategoryTheory.Limits.HasFiniteBiproductsFinite