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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:sSetG→sSet/ˉWG is a version of the Borel construction, BV=(V×WG)/G. This functor has an evident right adjoint defined by (Y→ˉWG)↦HomsSet/ˉWG(WG,Y), but they claim instead that it has a left adjoint defined by Y↦Y×ˉWGWG. Maybe I was up too late last night, but I cannot see why this is true; can someone enlighten me?
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