A 2-categorical equivariant fundamental groupoid is defined, and its discrete quotient is shown to be Morita invariant for representable orbifolds.
Atlases for Ineffective Orbifolds
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abstract
We give a definition of atlases for ineffective orbifolds, and prove that this definition leads to the same notion of orbifold as that defined via topological groupoids.
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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.