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created an entry Borel model structure for the standard (projective) model strucure for actions of simplicial groups on simplicial sets.
added a paragraph on the relation to the “genuine”/”fine” equivariant homotopy theory
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?
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