Definition of "category"

category

/ˈkætəˌɡɔɹi/

noun
plural categories
1. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
  Quotations
  The traditional way of describing the similarities and differences between constituents is to say that they belong to categories of various types. Thus, words like boy, girl, man, woman, etc. are traditionally said to belong to the category of Nouns, whereas words like a, the, this, and that are traditionally said to belong to the category of Determiners.
  1988, Andrew Radford, Transformational grammar: a first course, Cambridge, UK: Cambridge University Press, page 51
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.
  Quotations
  The use of the word ‘factor’ shows the explicit intention of categorists to work with functions in an algebraic manner: a category is an algebra of functions.
  1995, Michael Barr with Charles Wells, Category Theory for Computing Science‎, 2nd edition, Cambridge, Great Britain: Prentice Hall, §2.8.9, page 46