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nLab > Latest Changes: model structure for Segal categories

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2012

    at model structure for Segal categories I have very briefly added the basic definition, some basic properties, and added references.

    • CommentRowNumber2.
    • CommentAuthorZhen Lin
    • CommentTimeApr 8th 2013

    Silly question: Is a weak equivalence between fibrant objects in this model structure a categorical equivalence in the sense of the article, i.e. without applying the precategory-to-category completion functor? I can’t find any statement one way or the other…

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2013
    • (edited Apr 8th 2013)

    Yes, I think so.

    This follows under 2-out-of-3 from the characterizing def. 2.1 in Hirschowitz-Simpson (which says that completion is homotopy-idempotentent, in particular that the completion of a pre-Segal category which already is a Segal category is a weak equivalence).

    I haved aded a remark on this to the entry model structure for Segal categories now.

    (Maybe you feel inspired to fill in some more of the missing text in the entry.)

  4. fixed bulleted list

    diff, v9, current

1 to 4 of 4

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