The effectiveness conjecture for homotopy projectors on n-stacks

An $n$-stack is a functor on a site satisfying descent with respect to sieves, and $nSTACK/{\cal X}$ denotes the resulting higher category of $n$-stacks. Let $U'$ be an $n$-stack with an endomorphism $p:U'\to U'$ satisfying $p\circ p\sim p$, and let $T$ be the telescope construction of Section 5. Effectiveness conjecture. The homotopy projector is effective: the telescope construction $T$ is again an $n$-stack. The claim concerns closure of $n$-stacks under this homotopy-colimit construction, and no resolution is supplied.