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Atrium > Mathematics, Physics & Philosophy: a fourth use for the term "simplicial category"?

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    • CommentRowNumber1.
    • CommentAuthorjoe.hannon
    • CommentTimeJul 21st 2013

    At simplicial category, three meanings for the phrase are mentioned: the simplex category, a simplicial object in Cat, or an sSet-enriched category. Then at enriched category#examples, the phrase is apparently used to describe a category internal to sSet. Is this term overloaded a fourth time?

    By the way, what does it mean for a simplicial set to be discrete? All the cells above 0 are degenerate?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJul 21st 2013

    A category internal to sSet is actually the same as a simplicial object in Cat! I’ve added a remark to this effect.

    Yes, “discrete” means that all higher simplices are degenerate, or equivalently that it is constant as a functor to Set.

    • CommentRowNumber3.
    • CommentAuthorjoe.hannon
    • CommentTimeJul 23rd 2013

    Thank you, sir. That is a fun surprise.

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