N₂ — Mathlib

English

The functor N₁ extends to the Karoubi envelope of SimplicialObject, producing a functor N₂ which maps Karoubi(SimplicialObject C) to Karoubi(ChainComplex C ℕ).

Русский

Функтор N₁ расширяется до каруоби-области SimplicialObject, образуя функтор N₂, который переводит Karoubi(SimplicialObject C) в Karoubi(ChainComplex C ℕ).

LaTeX

$$$N_2 : \mathrm{Karoubi}(\mathrm{SimplicialObject}(C)) \longrightarrow \mathrm{Karoubi}(\mathrm{ChainComplex}(C, \mathbb{N}))$$$

Lean4

/-- The extension of `N₁` to the Karoubi envelope of `SimplicialObject C`. -/
@[simps!]
def N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ) :=
  (functorExtension₁ _ _).obj N₁

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