  We extend the notion of simplicial set with effective homology to diagrams of
simplicial sets. Further, for a given finite diagram of simplicial sets $X
\colon \mathcal{I} \to \mathsf{sSet}$ such that each simplicial set $X(i)$ has
effective homology, we present an algorithm computing the homotopy colimit
$\mathsf{hocolim} X$ as a simplicial set with effective homology. We also give
an algorithm computing the cofibrant replacement $X^\mathsf{cof}$ of $X$ as a
diagram with effective homology. This is applied to computing of equivariant
cohomology operations.
