Let $M$ and $N$ two very nice simplicial model categories and let $F:N\rightarrow M$ be a (nice) simplicial functor which induces an equivalence of homotopy categories, i.e. $Ho(F): Ho(N)\rightarrow Ho(M)$ is an equivalence of homotopy categories and it is well defined. We define the category $\pi\_{0}M$ as the category having the same objects of $M$ and $Hom\_{\pi\_{0}M}(a,b)=\pi\_{0}Map\_{M}(a,b)$.


What can we say about the functor $\pi\_{0}F:\pi\_{0}N\rightarrow \pi\_{0}M$? is it an equivalence of categories. Maybe we should assume that $F$ takes cofibrant-fibrant objects to cofibrant-fibrant objects... or something close to that. 


Clarification: A simplicial functor between simplicial model categories $M$ and $N$ is a simplicial enriched functor between simplicial enriched categories. 


Clarification II: A simplicial model category is a model category $M$ tensored and cotensored over the model category of simplicial sets in a way compatible with model structure of both model structure on $M$ and on simplicial sets.


**Edit** I think there is a counterexample: Let $M=N$ be the standard model category of simplicial sets, and let $F: sSet\rightarrow sSet$ be the functor of fibrant replacement such that it is simpllicial (I guess such functor do exist). Then $\pi\_{0}F$ is not an equivalence of categories, while $Ho(F)$ is. I'm I right ?



Simplicial model categories and simplicial equivalence
Since there is an answer to the question, I think I should write it down. 


There is a simple counterexample to my question: Let $M=N=sSet$ the standard model category of simplicial sets. Let $ex^{\infty}:sSet\rightarrow sSet$ the fibrant replacement functor. It is simplicial as it was noticed in the comments. $Ho(F)$ is well defined and induce an (auto)equivalence of the homotopy category $Ho(sSet)$. On the other hand $\pi\_{0}(F)$ is clearly not an autoequivalence of $\pi\_{0}sSet$. 


