Let $C$ be a model category and $\Delta$ be the simplex category. Denote by $Func(\Delta, C)$ the diagram category which has a Reedy model structure. Now let $X$ be a Reedy fibrant diagram in $Func(\Delta, C)$.
Then what are the necessary conditions for $X$ to be fibrant. I think one can show $X$ is pointwise fibrant. Is it also true that the maps $X_{n} \rightarrow X_{m}$ are fibrations in $C$.