Remark 1.5.5.10. Let $p: X \rightarrow Y$ be a trivial Kan fibration. Then, for every vertex $y$ of $Y$, the fiber $X \times _{Y } \{ y\} $ is a contractible Kan complex (this is a special case of Remark 1.5.5.2). For a partial converse, see Proposition 3.3.7.6.
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