English
From a factorization data of coprod.desc f (id Y) into a cofibration followed by a trivial fibration, one obtains a CofibrantBrownFactorization f.
Русский
Из данных факторизации coprod.desc f (id Y) в виде cofibration ∘ h и тривиальной фибрации получается CofibrantBrownFactorization f.
LaTeX
$$$\exists h' : MapFactorizationData(\operatorname{cofibrations} C)(\operatorname{trivialFibrations} C)(\mathrm{coprod.desc} f (\mathrm{id} Y)) \Rightarrow \text{CofibrantBrownFactorization } f$$$
Lean4
instance [WeakEquivalence f] : WeakEquivalence h.i :=
weakEquivalence_of_postcomp_of_fac h.fac
