Kerodon

Definition 5.5.1.1. Let $X$ be a simplicial set and let $\sigma : \Delta ^2 \rightarrow X$ be a $2$-simplex of $X$. We will say that $\sigma $ is left-degenerate if it factors through the map $\sigma ^{0}_{1}: \Delta ^2 \rightarrow \Delta ^1$ given on vertices by $\sigma ^{0}_{1}(0) = 0 = \sigma ^{0}_{1}(1)$ and $\sigma ^{0}_{1}(2) = 1$ (Notation 1.1.1.13). We say that $\sigma $ is right-degenerate if it factors through the map $\sigma ^{1}_{1}: \Delta ^2 \rightarrow \Delta ^1$ given on vertices $\sigma ^{1}_{1}(0) = 0$ and $\sigma ^{1}_{1}(1) = 1 = \sigma ^{1}_{1}(2)$.