sum' — Mathlib

English

In any category with zero morphisms, the bottom arrow in MonoOver is the zero morphism.

Русский

В любой категории с нулевыми морфизмами нижний стрелок в MonoOver равен нулю.

LaTeX

$$$\\mathrm{bot.arrow} = 0$ in MonoOver$$

Lean4

/-- The sum of two functors that land in a given category `C`. -/
def sum' : A ⊕ B ⥤ C
    where
  obj
    | inl X => F.obj X
    | inr X => G.obj X
  map {X Y} f := Sum.homInduction (inl := fun _ _ f ↦ F.map f) (inr := fun _ _ g ↦ G.map g) f
  map_comp {x y z} f g := by cases f <;> cases g <;> simp [← Functor.map_comp]
  map_id x := by cases x <;> (simp only [← map_id]; rfl)

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