Theorems · Theorem · category theory

CategoryTheory.leftDistributor_hom

∀ {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 : Fintype J] (X : C) (f : J → C),
  (CategoryTheory.leftDistributor X f).hom =
    ∑ j,
      CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.Limits.biproduct.π f j))
        (CategoryTheory.Limits.biproduct.ι (fun j => CategoryTheory.MonoidalCategoryStruct.tensorObj X (f j)) j)

Defined in

Mathlib.CategoryTheory.Monoidal.Preadditive

Cited by

4 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalPreadditiveCategoryTheory.Limits.HasFiniteBiproductsFintype