ScalingStacks

Proof. The result follows from definition 2.14, lemma 6.4 and from the universal property of Bousfield localization (see section 2.5: The functor $\phi$ preserves filtered colimits and by proposition 5.27 any split-exact sequence can be approximated by a filtered colimit of split-exact sequences in ${\mathcal{E}}$). ∎