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A structure on a set or, more generally, a type, consists of additional mathematical objects that in some manner attach (or are related) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.

A partial list of possible structures is measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, graphs, events, differential structures, categories, setoids, and equivalence relations.