Theorems · Theorem · category theory

CategoryTheory.Limits.biproduct.matrix_desc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {J K : Type}
  [inst_2 : Finite J] [inst_3 : CategoryTheory.Limits.HasFiniteBiproducts C] [inst_4 : Fintype K] {f : J → C}
  {g : K → C} (m : (j : J) → (k : K) → f j ⟶ g k) {P : C} (x : (k : K) → g k ⟶ P),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biproduct.matrix m)
      (CategoryTheory.Limits.biproduct.desc x) =
    CategoryTheory.Limits.biproduct.desc fun j => ∑ k, CategoryTheory.CategoryStruct.comp (m j k) (x k)

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveFiniteCategoryTheory.Limits.HasFiniteBiproductsFintype