I have a question about a definition used in nLab article on $n$-groupoids: <https://ncatlab.org/nlab/show/n-groupoid>


What does it mean that "every parallel pair of $j$-morphisms is equivalent for $j>n$? Surely, that's not a research question, but I nowhere found an answer. Does that mean that the corresponending equilizers on $j$-level are equivalences? (just a guess of mine)



Equivalent parallel pair of $j$-morphisms
It means that between every two $j$-cells with the same domain and codomain ($j > n$), there is a $(j + 1)$-cell between them (which is necessarily an equivalence by the first condition of the definition on that page) exhibiting them as equivalent.


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