Example 10.2.3.11. Let $X_{\bullet }$ be a simplicial object of an $\infty $-category $\operatorname{\mathcal{C}}$. For small values of $k$, the degeneracy cube $\sigma _{k}: \operatorname{\raise {0.1ex}{\square }}^{k} \rightarrow \operatorname{\mathcal{C}}$ of Construction 10.2.3.10 can be described more concretely:
The degeneracy cube $\sigma _0$ can be identified with the object $X_0$ of $\operatorname{\mathcal{C}}$.
The degeneracy cube $\sigma _1$ can be identified with the degeneracy operator $s^{0}_{0}: X_0 \rightarrow X_1$ of Notation 10.2.0.4.
The degeneracy cube $\sigma _{2}$ is a square diagram
\[ \xymatrix@R =50pt@C=50pt{ X_0 \ar [r]^{ s^{0}_{0} } \ar [d]^{s^{0}_{0} } & X_1 \ar [d]^{ s^{1}_{0} } \\ X_1 \ar [r]^{ s^{1}_{1} } & X_{2} } \]which witnesses the identity $[ s^{1}_{0} ] \circ [s^{0}_{0} ] = [ s^{1}_{1} ] \circ [s^{0}_{0} ]$ in the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$.