English
The application of the N₁ construction to Γ₀ at a chain complex K yields a natural isomorphism between the N₁ and Γ₀-constructions evaluated on K.
Русский
Применение конструкции N₁ к Γ₀ в отношении цепного комплекса K даёт естественное изоморождение между N₁ и Γ₀, оцениваемыми на K.
LaTeX
$$$N_1\Gamma_0\text{ app } K \cong \text{(Γ₀.splitting_K).toKaroubiNondegComplexIsoN₁}$$$
Lean4
/-- The functor `SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)` which maps
`X` to the formal direct factor of `K[X]` defined by `PInfty`. -/
@[simps]
def N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)
where
obj
X :=
{ X := AlternatingFaceMapComplex.obj X
p := PInfty
idem := PInfty_idem }
map f := { f := PInfty ≫ AlternatingFaceMapComplex.map f }
