Remark 3.5.6.2. Let $n$ be a nonnegative integer and let $f: X \rightarrow Y$ be a morphism of Kan complexes which exhibits $Y$ as a fundamental $n$-groupoid of $X$. Then $f$ is a Kan fibration (Corollary 3.5.5.14). In particular, since it is surjective on vertices, it is surjective on $m$-simplices for every integer $m$ (see Remark 3.1.2.8).

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