Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The category of reduced orbifolds in local charts   It is well-known that reduced smooth orbifolds and proper effective foliation
Lie groupoids form equivalent categories. However, for certain recent lines of
research, equivalence of categories is not sufficient. We propose a notion of
maps between reduced smooth orbifolds and a definition of a category in terms
of marked proper effective \'etale Lie groupoids such that the arising category
of orbifolds is isomorphic (not only equivalent) to this groupoid category.

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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an