cechNerve — Mathlib

English

There exists a natural equivalence between morphisms from Augmented to Arrow X→F and morphisms from X to F’s augmented Čech nerve.

Русский

Существует естественное эквивалентность между морфизмами Augmented→F и X→F.augmentedCechNerve.

LaTeX

$$$ (X ⟶ F.augmentedCechNerve) \\simeq (Augmented.X ⟶ F) $$$

Lean4

/-- The Čech nerve construction, as a functor from `Arrow C`. -/
@[simps]
def cechNerve : Arrow C ⥤ SimplicialObject C where
  obj f := f.cechNerve
  map F := Arrow.mapCechNerve F

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