Mathematical Sciences Classification System
18Dxx - Categories with structure
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18D05Double categories, $2$-categories, bicategories and generalizations
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18D10Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
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18D15Closed categories (closed monoidal and Cartesian closed categories, etc.)
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18D20Enriched categories (over closed or monoidal categories)
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18D25Strong functors, strong adjunctions
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18D30Fibered categories
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18D35Structured objects in a category (group objects, etc.)
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18D50Operads [See also 55P48]
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18D99None of the above, but in this section