I've learned the theorem when reading a comment by Vidit Nanda to my question [see here][1].
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][2]


**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][3] (lemma 26, case (3))


  [1]: https://mathoverflow.net/questions/220930/fiber-homotopy-fiber-of-spaces
  [2]: http://ac.els-cdn.com/0166864186900180/1-s2.0-0166864186900180-main.pdf?_tid=413cfece-735f-11e5-8bbb-00000aab0f01&acdnat=1444929045_1e6b9674d9340b54c48ceb2b5f051c8b
  [3]: http://www.di.ens.fr/~colin/textes/08helly.pdf