additive_ofFullyFaithful — Mathlib

English

Composing the preadditive Yoneda embedding with the forgetful whiskering equals the regular Yoneda embedding.

Русский

Сложение предаддитивных Yoneda-встроек с забывающим whiskering даёт обычную Yoneda-встройку.

LaTeX

$$$preadditiveYoneda \circ whiskering = yoneda$$$

Lean4

/-- The preadditive structure on `C` induced by a fully faithful functor `F : C ⥤ D` makes `F` an
additive functor. -/
theorem additive_ofFullyFaithful :
    letI : Preadditive C := Preadditive.ofFullyFaithful hF
    F.Additive :=
  letI : Preadditive C := Preadditive.ofFullyFaithful hF
  { map_add := by simp [Equiv.add_def] }

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