English
Fibrations are stable under base change, i.e., pullbacks of fibrations along any morphism are fibrations.
Русский
Фибрации устойчивы к базовым изменениям, то есть расходования фибраций по произвольному морфизму являются фибрациями.
LaTeX
$$$\\operatorname{IsStableUnderBaseChange}(\\mathrm{fibrations}(C)).$$$
Lean4
instance [(trivialFibrations C).IsStableUnderBaseChange] [Fibration f] [WeakEquivalence f] :
WeakEquivalence (pullback.snd f g) := by
rw [weakEquivalence_iff]
exact (MorphismProperty.of_isPullback (IsPullback.of_hasPullback f g) (mem_trivialFibrations f)).2
