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    • 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.)