Suppose we have an adjunction of categories $F:M\leftrightarrow N:U$. We define the associated (co)monad $G=F\circ U$. For any object $x\in N$ we define the simplicial resolution of x given by $$G_{\bullet}(x)=\dots  G^{2}(x)\rightrightarrows G(x)$$
I was wondering if $colim_{n} G_{n}(x)=x$ ?