Often, category theorists refer to a quasi-category as "discrete". I found only the following formal definition for this term, which I find quite puzzling:
A simplicial set $X$ is discrete if every morphism in $\Delta$ induces a bijection on the sections of $X$.
Is this the common definition for a discrete quasi-category? How does this catch the intuition of a category being "uninteresting" in some sense? I'd be happy to get a more detailed definition.
It means that the only higher-dimensional simplices are iterated degeneracies of $0$-simplices, so that the simplicial set “looks like” a discrete topological space.