English
The augmented Čech conerve construction is a functor from Arrow C to CosimplicialObject.Augmented C; on objects it sends f to f.augmentedCechConerve and on arrows it sends F to Arrow.mapAugmentedCechConerve F.
Русский
Укoганная Čech-конверва — это функтор от Arrow C к CosimplicialObject.Augmented C; на объектах она отправляет f в f.augmentedCechConerve, а на стрелках — F в Arrow.mapAugmentedCechConerve F.
LaTeX
$$$\\mathrm{augmentedCechConerve} : \\mathrm{Arrow}(C) \\to \\mathrm{CosimplicialObject.Augmented}(C),\\quad \\mathrm{augmentedCechConerve}(f) = f.augmentedCechConerve,\\; \\mathrm{augmentedCechConerve}(F) = \\mathrm{Arrow.mapAugmentedCechConerve}(F)$$$
Lean4
/-- The augmented Čech conerve construction, as a functor from `Arrow C`. -/
@[simps]
def augmentedCechConerve : Arrow C ⥤ CosimplicialObject.Augmented C
where
obj f := f.augmentedCechConerve
map F := Arrow.mapAugmentedCechConerve F
