nLab (n,0)-category

An $(n,0)$-category is an (n,r)-category that is an n-groupoid.

By the general rules of $(n,r)$-categories, an $(n,0)$-category is an $\infty$-category such that * any $j$-morphism is an equivalence, for $j \gt 0$; * any two parallel $j$-morphisms are equivalent, for $j \gt n$.

You can start from any notion of $\infty$-category, strict or weak; up to equivalence, the result is the same as an n-groupoid with a corresponding level of strictness.