Lemma 3.2.4.11. Let $X$ be a Kan complex and let $0 \leq i \leq n$ be integers with $n > 0$. Then every morphism $\sigma _0: \Lambda ^{n}_{i} \rightarrow X$ is nullhomotopic.
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Lemma 3.2.4.11. Let $X$ be a Kan complex and let $0 \leq i \leq n$ be integers with $n > 0$. Then every morphism $\sigma _0: \Lambda ^{n}_{i} \rightarrow X$ is nullhomotopic.
Proof. Since $X$ is a Kan complex, we can extend $\sigma _0$ to an $n$-simplex $\sigma : \Delta ^ n \rightarrow X$. By virtue of Remark 3.2.4.10, it will suffice to show that $\sigma $ is nullhomotopic, which is a special case of Exercise 3.2.4.8. $\square$