Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.lift_desc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C}
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] {T U : C} {f : T ⟶ X} {g : T ⟶ Y} {h : X ⟶ U} {i : Y ⟶ U},
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.lift f g) (CategoryTheory.Limits.biprod.desc h i) =
    CategoryTheory.CategoryStruct.comp f h + CategoryTheory.CategoryStruct.comp g i

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

7 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct