A simplicial object in is a particular case of simplicial object, of course, with the there being . It therefore has a simplicial set of objects and a simplicial set of morphisms. This is equivalent to giving an internal category in simplicial sets.
Remark A simplicial object in is sometimes called a simplicial category, but that has other meanings.
simplicial object in Cat
One of the few references that discusses a model category structure on as opposed to just is
A model category sturcture on presenting (infinity,1)-categories is in
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