On d-categories and d-operads

We extend the theory of d-categories, which are a strict model for (d, 1)-categories introduced by Lurie, by providing an explicit description of the right mapping spaces of the d-homotopy category of an ∞-category. Using this description, we deduce an invariant ∞-categorical characterization of the d-homotopy category. We then proceed to develop an analogous theory of d-operads, which model ∞-operads with (d-1)-truncated multimapping spaces, and prove analogous results for them.