TITLE: Vietoris-Begle theorem for simplicial sets
QUESTION [9 upvotes]: I've learned the theorem when reading a comment by Vidit Nanda to my question see here.
Here is the (simplified) version of the theorem for topological spaces:
Vietoris-Begle Theorem
Let $f:X\rightarrow Y$ be a surjective closed continuous map between paracompact Hausdorff spaces. Assume that for any $y\in Y$, $f^{-1}(y)$ is weakly contractible, then the induced map
$$H^{\ast}(f): H^{\ast}(Y,G)\rightarrow H^{\ast}(X,G)$$ 
is an isomorphism (reduced cohomology) for any abelian group $G$. 
It seems that the assumption that $f$ is closed is essential. 
My question is the following: Do we have a simplicial version of Vietoris-Begle Theorem ? i.e., 
simplicial Vietoris-Begle Theorem ?
Let $f:X\rightarrow Y$ be a surjective morphism of simplicial sets (Kan complexes). Assume that for any $y\in Y_{0}$, $f^{-1}(y)$ is weakly contractible simplicial sets, then the induced map
$$H^{\ast}(f): H^{\ast}(Y,G)\rightarrow H^{\ast}(X,G)$$ 
is an isomorphism (reduced cohomology) for any abelian group $G$.
reference for the topological case: reference
Edit: Please feel free to add more conditions on $f,X ,Y$ but not the trivial ones such as $f$ is a fibration or something similar...
There is for example a simplicial (strong) version here (lemma 26, case (3))

REPLY [6 votes]: Here is a theorem due (I think) to E. Dror Farjoun (it is Theorem 9.A.11 in his book on homotopy localization).
Theorem: Let  $f:X\to Y$ be a surjective map of connected pointed simplicial sets.  Then the homotopy fiber $F_f$ of $f$ is in the smallest closed class containing $f^{-1}(\sigma)$ for every simplex $\sigma$ in $Y$.
A closed class is a class $\mathcal{C}$ of spaces which is closed under weak equivalence and (pointed) homotopy colimit.  For pointed spaces use pointed homotopy colimit; for unpointed ones, restrict to homotopy colimits of diagrams whose nerve is contractible.
It follows, in particular, if every $f^{-1}(\sigma)$ is weakly contractible, then $f$ will be a weak homotopy equivalence (Corollary 9.B.3.1).