Theorems · Theorem · category theory

CategoryTheory.Limits.biproduct.lift_matrix

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