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What is a category?

What is a category? Here are some definitions.

Noun
  1. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
  2. (mathematics) A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.
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Examples
In reality, Vin de Pays is the second tier of the French quality hierarchy and the category just above basic vin de table.
Within this category American tycoons probably merit their own subsection, as do, quite separately, conmen and speculators.
The 19-year-old wowed the judges by styling her model with a red Mohawk style in the Junior Ladies Fashionable Day Style category.
Each category contains several subcategories while assessment exercises and instruments exist to identify individual students' particular style.
You'll also want to consider a DVD burner, and of course a CD-RW drive is a must for this category.
Gangsta rap is generally considered a subgenre of the larger category of rap music, which itself is a subcategory of hip-hop.

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