In the paper DDK80 cited at Borel model structure, the equivalence functor $B :sSet^G \to sSet / \overline{W}G$ is a version of the Borel construction, $B V = (V \times W G)/G$. This functor has an evident *right* adjoint defined by $(Y\to \overline{W}G) \mapsto Hom_{sSet/\overline{W}G}(W G,Y)$, but they claim instead that it has a *left* adjoint defined by $Y\mapsto Y \times_{\overline{W}G} W G$. Maybe I was up too late last night, but I cannot see why this is true; can someone enlighten me?

added a paragraph on the relation to the “genuine”/”fine” equivariant homotopy theory

]]>created an entry *Borel model structure* for the standard (projective) model strucure for actions of simplicial groups on simplicial sets.