Warning 3.3.3.9. Let $u: X \rightarrow Y$ be a morphism of braced simplicial sets. If $u$ does not carry nondegenerate simplices of $X$ to nondegenerate simplices of $Y$, then the diagram of topological spaces
\[ \xymatrix@R =50pt@C=50pt{ | \operatorname{Sd}(X) | \ar [r]^-{ f_ X } \ar [d]^{ | \operatorname{Sd}(u) |}_-{\sim } & | X | \ar [d]^{ | u | } \\ | \operatorname{Sd}(Y) | \ar [r]^-{ f_ Y}_-{\sim } & | Y | } \]
does not necessarily commute (this phenomenon occurs already in the case where $X$ and $Y$ are simplices: see Remark 3.3.2.4).