Theorems · Theorem · category theory

CategoryTheory.Biprod.ofComponents_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {X₁ X₂ Y₁ Y₂ Z₁ Z₂ : C} (f₁₁ : X₁ ⟶ Y₁) (f₁₂ : X₁ ⟶ Y₂)
  (f₂₁ : X₂ ⟶ Y₁) (f₂₂ : X₂ ⟶ Y₂) (g₁₁ : Y₁ ⟶ Z₁) (g₁₂ : Y₁ ⟶ Z₂) (g₂₁ : Y₂ ⟶ Z₁) (g₂₂ : Y₂ ⟶ Z₂),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Biprod.ofComponents f₁₁ f₁₂ f₂₁ f₂₂)
      (CategoryTheory.Biprod.ofComponents g₁₁ g₁₂ g₂₁ g₂₂) =
    CategoryTheory.Biprod.ofComponents
      (CategoryTheory.CategoryStruct.comp f₁₁ g₁₁ + CategoryTheory.CategoryStruct.comp f₁₂ g₂₁)
      (CategoryTheory.CategoryStruct.comp f₁₁ g₁₂ + CategoryTheory.CategoryStruct.comp f₁₂ g₂₂)
      (CategoryTheory.CategoryStruct.comp f₂₁ g₁₁ + CategoryTheory.CategoryStruct.comp f₂₂ g₂₁)
      (CategoryTheory.CategoryStruct.comp f₂₁ g₁₂ + CategoryTheory.CategoryStruct.comp f₂₂ g₂₂)

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts