I have had a problem I've been thinking of recently but can't seem to make anything of it.
Let $X$ be a simplicial set. It is well known that one can construct a Postnikov tower
$$P_nX \rightarrow P_{n-1}X \rightarrow \cdots \rightarrow P_1 X \rightarrow P_0 X$$
of X through , for example, letting $P_n$ be the $n$-th coskeleton of $X$. If $X$ is a (pointed) fibrant simplicial set, the above tower is actually a tower of fibrations.
When we have a cosimplicial space $Y$ which we assume to be pointed fibrant in the Reedy model structure, we also have the Tot-tower $$Tot_n Y \rightarrow Tot_{n-1} Y \rightarrow \cdots \rightarrow Tot_1 Y \rightarrow Tot_0 Y$$ which is a tower of fibrations as well.
The question I have been having is the following:
Given a fibrant simplicial set $X$ as above, can we recover the Postnikov tower of $X$ as some sort of totalization of some cosimplicial space? I would prefer if there were a somewhat canonical way to do this.