ScalingStacks

Lemma 7.5. If $U\xrightarrow{f}V\xrightarrow{g}W$ are maps of Segal spaces such that $f$ and $g$ are Dwyer-Kan equivalences, then $gf$ is a Dwyer-Kan equivalence.

If $U\xrightarrow{f}V\xrightarrow{g}W\xrightarrow{h}X$ are maps of Segal spaces such that $gf$ and $hg$ are Dwyer-Kan equivalences, then each of the maps $f$, $g$, and $h$ is a Dwyer-Kan equivalence.