# Kerodon

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Definition 2.3.2.3. Let $X_{\bullet }$ be a simplicial set. We will say that a $2$-simplex $\sigma$ of $X_{\bullet }$ is thin if it satisfies the following condition:

$(\ast )$

Let $n \geq 3$, let $0 < i < n$, and let $\tau$ denote the $2$-simplex of $\Lambda ^{n}_{i}$ given by the map

$[2] \simeq \{ i-1, i, i+1 \} \subseteq [n].$

Then any map of simplicial sets $f_0: \Lambda ^{n}_{i} \rightarrow X_{\bullet }$ satisfying $f_0( \tau ) = \sigma$ can be extended to an $n$-simplex of $X_{\bullet }$.