sum — Mathlib

English

Let α : F ⟶ G and β : H ⟶ I with X ∈ A ⊕ C. Then (sum α β).app (inl a) = (inl) .map (α.app a).

Русский

Пусть α : F ⟶ G и β : H ⟶ I; для X ∈ A ⊕ C выполняется (sum α β).app (inl a) = (Sum.inl) .map (α.app a).

LaTeX

$$$ (\\sum α β).app (\\mathrm{inl}\\, a) = (\\mathrm{inl}_ B D).map (α.app a) $$$

Lean4

/-- The sum of two natural transformations. -/
def sum {F G : A ⥤ B} {H I : C ⥤ D} (α : F ⟶ G) (β : H ⟶ I) : F.sum H ⟶ G.sum I
    where
  app
    X :=
    match X with
    | inl X => (Sum.inl_ B D).map (α.app X)
    | inr X => (Sum.inr_ B D).map (β.app X)
  naturality X Y f := by cases f <;> simp [← Functor.map_comp]

Похожие утверждения