Theorems · Theorem · category theory

CategoryTheory.Functor.map_sum

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Preadditive C]
  [inst_3 : CategoryTheory.Preadditive D] (F : CategoryTheory.Functor C D) [F.Additive] {X Y : C} {α : Type u_4}
  (f : α → (X ⟶ Y)) (s : Finset α), F.map (∑ a ∈ s, f a) = ∑ a ∈ s, F.map (f a)

Defined in

Mathlib.CategoryTheory.Preadditive.AdditiveFunctor

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.Functor.Additive