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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 15th 2014

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

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 15th 2014

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

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJan 2nd 2015

    In the paper DDK80 cited at Borel model structure, the equivalence functor B:sSet GsSet/W¯GB :sSet^G \to sSet / \overline{W}G is a version of the Borel construction, BV=(V×WG)/GB V = (V \times W G)/G. This functor has an evident right adjoint defined by (YW¯G)Hom sSet/W¯G(WG,Y)(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 YY× W¯GWGY\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?