First of all let me define what homotopy colimit i'm talking about. Let F be a functor from a small category to the category of simplicial set, the homotopy colimit is the simplicial realization of the simplicial replacement of the functor F.
So it is a simplicial set and its skeleton can be given by $|X|^k = \coprod^k_{n=0} X_n \times \Delta[n]/\sim$ where $\sim$ is the usual identifications.
My question is do we have in this case a pushout square (similar to the geometric realization, but here i do simplicial realization since i want to have a simplicial set at the end)
$X_k \times \Delta[k]\leftarrow X_k \times \partial \Delta[k] \rightarrow |X|^{k-1}$ and one can build the skeleton $[X|^k$ in iterative way?
