It is well-known that reduced smooth orbifolds and proper effective foliationLie groupoids form equivalent categories. However, for certain recent lines ofresearch, equivalence of categories is not sufficient. We propose a notion ofmaps between reduced smooth orbifolds and a definition of a category in termsof marked proper effective \'etale Lie groupoids such that the arising categoryof orbifolds is isomorphic (not only equivalent) to this groupoid category.
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