A 2-categorical equivariant fundamental groupoid is defined, and its discrete quotient is shown to be Morita invariant for representable orbifolds.
Buckley, Fibred 2-categories and bicategories, Journal of Pure and Applied Algebra 218 (2014), pp
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The Equivariant Fundamental Groupoid as an Orbifold Invariant
A 2-categorical equivariant fundamental groupoid is defined, and its discrete quotient is shown to be Morita invariant for representable orbifolds.