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    • CommentRowNumber1.
    • CommentAuthorZhen Lin
    • CommentTimeAug 3rd 2013

    I started a page about the simplicial bar construction. I haven’t checked all the details carefully (especially regarding 𝒱\mathcal{V}-naturality!) though.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeAug 3rd 2013

    Just one point, is ’geometric realization’ really a good term for something where there is no necessity for the resulting objects to have any geometric nature. Perhaps some term such as \mathcal{M}-realization with a note that in cases such as …. this is the geometric realization.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 3rd 2013
    • (edited Aug 3rd 2013)

    Or perhaps just call it ’realization’ (or ’realisation’ as the case may be).

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeAug 3rd 2013

    @Tim: Maybe not, but isn’t it pretty well established? Even the classical case of the geometric realization of a simplicial set as a topological space doesn’t have any “geometry” in the sense I usually think of the word, only a topology.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 3rd 2013

    Really, geometric realization is the established term even when the receiving category isn’t a good category of (topological) spaces?

    We do have this page nerve and realization, to which we can point for more general situations.

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeAug 3rd 2013

    The term realisation is used for this on the page , nerve and realization, so perhaps should be used here. The general situation is very well handled there.

    • CommentRowNumber7.
    • CommentAuthorZhen Lin
    • CommentTimeAug 3rd 2013

    I replaced ‘geometric realisation’ with ‘realisation’ and fixed a little error in the statement of the hocolim theorem.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeAug 4th 2013

    I’ve always heard it called “geometric realization” in at least some other situations, like spectra. But it doesn’t matter.

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