described in [@SergerGenova; @polypost]. In many cases, only minor and/or straightforward modifications are needed. One exception is the equivariant effective homology of Moore–Postnikov stages, for which we rely on a separate paper [@Vokrinek].

Compared to our previous work [@CKMSVW11], the main new ingredient is the weakening of the [H-]{}space structure that exists on Moore–Postnikov stages. This is needed in order to carry out the whole computation algorithmically. Accordingly, the construction of this structure is much more abstract. In [@CKMSVW11] we had $B=*$ and Postnikov stages carried a unique basepoint. In the case of nontrivial $B$, the basepoints are replaced by sections and Moore–Postnikov stages may not admit a section at all – this is related to the possibility of $[X,Y]^A_B$ being empty. Even if a section exists, it might be non-unique and consequently, the addition on ${{P_{{n}}}}$ will not preserve it in general. This is the origin of the above weakening. A further complication emerging from the non-uniqueness of the section is that it might happen that in the stage ${{P_{{{n}}-1}}}$ we choose a section which does not lift to ${{P_{{n}}}}$. In that case, we need to change the section of ${{P_{{{n}}-1}}}$ and compute everything again from scratch.

Plan of 