Remark 1.5.6.3. In the situation of Corollary 1.5.6.2, one can think of the simplicial set
\[ Z = \operatorname{Fun}( \Delta ^2, \operatorname{\mathcal{C}}) \underset {\operatorname{Fun}( \Lambda ^2_1, \operatorname{\mathcal{C}}) }{\times } \{ (g, \bullet , f) \} \]
as a “parameter space” for all choices of $2$-simplex $\sigma $ satisfying $d^{2}_0(\sigma ) = g$ and $d^{2}_2(\sigma ) = f$ (note that such $2$-simplices can be identified with the vertices of $Z$).