It is shown in Remark 7.1.12 of (a newer version of) Mark Hovey's book *Model Categories* that, in a stable model category, homotopy pullback squares coincide with homotopy pushout squares. The argument goes as follows: given a square $S$ of the form
$$
\begin{matrix}
W & \to & X\\
\downarrow_h & & \downarrow_g\\
Z & \to & Y
\end{matrix}
$$
one shows that $S$ is a pullback square if and only if the induced map $\mathrm{HoFibre}(h)\to\mathrm{HoFibre}(g)$ is an isomorphism in the homotopy category. Similarly, $S$ is a pushout square if and only if the induced map $\mathrm{HoCofibre}(h)\to\mathrm{HoCofibre}(g)$ is an isomorphism in the homotopy category. One concludes by observing that $\mathrm{HoCofibre}(h)$ is the suspension of $\mathrm{HoFibre}(h)$ and similarly for $g$.

**Question:** *Is it possible to generalize this statement to say something like as follows?*

"In a diagram of the form $$ \begin{matrix} W & & \to && X\\ &\searrow & \\ \downarrow &&Y&&\downarrow\\ &&&\searrow\\ Z & &\to && V, \end{matrix} $$ $V$ is a homotopy colimit of $$ \begin{matrix} W & & \to && X\\ &\searrow & \\ \downarrow &&Y&&\\ &&&\\\ Z & & && \end{matrix} $$ if and only if $W$ is a homotopy limit of $$ \begin{matrix} & & && X\\ & & \\ &&Y&&\downarrow\\ &&&\searrow\\ Z & &\to && V." \end{matrix} $$