In a usual category $\mathcal{C}$ one can pull the colim out of the Hom like this:$\DeclareMathOperator{\Hom}{Hom}\DeclareMathOperator{\colim}{colim}\DeclareMathOperator{\hocolim}{hocolim}\DeclareMathOperator{\Ho}{Ho}\DeclareMathOperator{\holim}{holim}$ $\Hom\nolimits_\mathcal{C}(\colim A_i,B)=\lim \Hom\nolimits_\mathcal{C}(A_i,B)$
I am looking for a corresponding statement for hocolims - lets say in simplicial sets, but if there are more general statements, that's even better.
E.g. I could imagine $\Hom\nolimits_{\mathcal{C}}(\hocolim A_i,B)=\lim \Hom\nolimits_{\Ho(\mathcal{C})}(A_i,B)$ - maybe one needs to have $B$ fibrant and the A_i cofibrant here, i.e. that the Homs on the right are $\mathbb{R}Homs$.
Using the internal Hom in simplicial sets I could also imagine versions like this: $\Hom(\colim A_i,B)=\holim \Hom(A_i,B)$ $\Hom(\colim A_i,B)=\holim \mathbb{R}\!\Hom(A_i,B)$
What is the right statement and what is the place to learn this hocolim-yoga?
Thanks! N.B.