Remark 5.5.1.2. Let $X$ be a simplicial set. Then:

A $2$-simplex $\sigma $ of $X$ is degenerate (in the sense of Definition 1.1.3.2) if and only if it is either left-degenerate or right-degenerate.

A $2$-simplex $\sigma $ of $X$ is constant (that is, factors through the projection map $\Delta ^2 \rightarrow \Delta ^0$) if and only if it is both left-degenerate and right-degenerate.

A $2$-simplex $\sigma $ of $X$ is left-degenerate if and only if it is right-degenerate when viewed as a $2$-simplex of the opposite simplicial set $X^{\operatorname{op}}$.