Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.lift_desc_assoc

∀ {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}
  {Z : C} (h_1 : U ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.lift f g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.desc h i) h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f h + CategoryTheory.CategoryStruct.comp g i)
      h_1

Defined in: Mathlib.CategoryTheory.Preadditive.Biproducts
Cited by: 0 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproduct

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Limits.biprodstatement · cited by 312
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.biprod.liftstatement and proof · cited by 79
CategoryTheory.Limits.biprod.descstatement and proof · cited by 54
CategoryTheory.Limits.biprod.lift_descproof · cited by 7

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