  Quasi-Gr\"obner categories were introduced by Sam and Snowden to unify
treatment of categories in representation stability. We give new examples of
quasi-Gr\"obner categories. Most of these categories are operadic categories of
Batanin and Markl which are used to encode homotopy coherent structures. This
suggests that other operadic categories might also be quasi-Gr\"obner.
Additionally, we show that set-operads form a full subcategory of the category
of operadic categories. We state several open problems.
