Cat"e*go*ry (?), n.; pl. Categories (#). [L. categoria, Gr. &?;, fr. &?; to accuse, affirm, predicate; &?; down, against + &?; to harrangue, assert, fr. &?; assembly.] 1. (Logic.) One of the highest classes to which the objects of knowledge or thought can be reduced, and by which they can be arranged in a system; an ultimate or undecomposable conception; a predicament.

The categories or predicaments -- the former a Greek word, the latter its literal translation in the Latin language -- were intended by Aristotle and his followers as an enumeration of all things capable of being named; an enumeration by the summa genera i.e., the most extensive classes into which things could be distributed.
J. S. Mill.

2. Class; also, state, condition, or predicament; as, we are both in the same category.

There is in modern literature a whole class of writers standing within the same category.
De Quincey.

• A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
        This steep and dangerous climb belongs to the most difficult category.
        I wouldn't put this book in the same category as the author's first novel.
  
• (mathematics) A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow.
        One well-known category has sets as objects and continous functions as arrows.