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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?
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.
Thank you, sir. That is a fun surprise.
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