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The term Lie $2$-groupoid is used in the literature in more than one context. Some examples are given below: Ginot and Stiénon's paper $G$-gerbes, principal $2$-group bundles and characteristic ...

I have made the following observation (hopefully a correct one) when reading the paper Orbifolds as stacks: They start with the strict $2$-category category of Lie groupoids, functors, natural ...