Variant 3.5.1.15. Let $f: X \rightarrow Y$ be a morphism of simplicial sets and let $n$ be a nonnegative integer. Using Proposition 3.1.7.1, we can choose a commutative diagram
3.66
\begin{equation} \begin{gathered}\label{equation:n-connective-for-simplicial-set} \xymatrix@R =50pt@C=50pt{ X \ar [r] \ar [d]^{f} & X' \ar [d]^{f'} \\ Y \ar [r] & Y', } \end{gathered} \end{equation}
where $X'$ and $Y'$ are Kan complexes and the horizontal maps are weak homotopy equivalences. We will say that $f$ is $n$-connective if the morphism of Kan complexes $f'$ is $n$-connective, in the sense of Definition 3.5.1.13. It follows from Remark 3.5.1.14 that this condition does not depend on the choice of the diagram (3.66).