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Categories with structure

18D05 Double categories, $2$-categories, bicategories and generalizations
18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
18D20 Enriched categories (over closed or monoidal categories)
18D25 Strong functors, strong adjunctions
18D30 Fibered categories
18D35 Structured objects in a category (group objects, etc.)
18D50 Operads [See also 55P48]
18D99 None of the above, but in this section 

Version of December 15, 1998