Variant 11.9.3.3. Let $X$ be the inverse limit of a tower of simplicial sets
\[ \cdots \xrightarrow {q_3} X(3) \xrightarrow {q_2} X(2) \xrightarrow {q_1} X(1) \xrightarrow {q_0} X(0). \]
If each of the morphisms $q_ n$ is a trivial Kan fibration, then the canonical map $q: X \rightarrow X(0)$ is a trivial Kan fibration.