category

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A specifically defined division in a system of classification; a class.
• noun A general class of ideas, terms, or things that mark divisions or coordinations within a conceptual scheme, especially.
• noun Aristotle's modes of objective being, such as quality, quantity, or relation, that are inherent in everything.
• noun Kant's modes of subjective understanding, such as singularity, universality, or particularity, that organize perceptions into knowledge.
• noun A basic logical type of philosophical conception in post-Kantian philosophy.
• noun A property or structural unit of a language, such as a part of speech or a type of phrase.
• noun A specific grammatical defining property of a linguistic unit or class, such as number or gender in the noun and tense or voice in the verb.
• noun Mathematics A class of objects, together with a class of morphisms between those objects, and an associative composition rule for those morphisms. Categories are used to study a wide variety of mathematical constructions in a similar way.

from The Century Dictionary.

• noun In logic, a highest notion, especially one derived from the logical analysis of the forms of proposition.
• noun A summum genus, or widest class.
• noun Any very wide and distinctive class; any comprehensive division or class of persons or things.

from the GNU version of the Collaborative International Dictionary of English.

• noun (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.
• noun Class; also, state, condition, or predicament.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
• noun 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.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a general concept that marks divisions or coordinations in a conceptual scheme
• noun a collection of things sharing a common attribute