Theorems · Theorem · category theory

CategoryTheory.Functor.Additive.map_add

∀ {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} [self : F.Additive] {X Y : C} {f g : X ⟶ Y},
  F.map (f + g) = F.map f + F.map g

the addition of two morphisms is mapped to the sum of their images

Defined in

Mathlib.CategoryTheory.Preadditive.AdditiveFunctor

Cited by

1 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.Additive