English
For a CofibrantBrownFactorization h of f, the map h.i is a weak equivalence provided f is a weak equivalence.
Русский
Для CofibrantBrownFactorization h от отображения f, если f — слабое эквалюид, то h.i — слабое экивалентное отображение.
LaTeX
$$$[\WeakEquivalence f] \Rightarrow \WeakEquivalence h.i$$$
Lean4
instance : MorphismProperty.IsWeakFactorizationSystem (cofibrations C) (trivialFibrations C) :=
MorphismProperty.IsWeakFactorizationSystem.mk' _ _
(fun {A B X Y} i p hi hp ↦ by
rw [mem_trivialFibrations_iff] at hp
rw [← cofibration_iff] at hi
have := hp.1
have := hp.2
infer_instance)
