a classificatory division in any field of knowledge, as a phylum or any of its subdivisions in biology.
3.
Metaphysics.
a.
(in Aristotelian philosophy) any of the fundamental modes of existence, such as substance, quality, and quantity, as determined by analysis of the different possible kinds of predication.
b.
(in Kantian philosophy) any of the fundamental principles of the understanding, as the principle of causation.
c.
any classification of terms that is ultimate and not susceptible to further analysis.
4.
categories. Also called Guggenheim.(used with a singular verb) a game in which a key word and a list of categories, as dogs, automobiles, or rivers, are selected, and in which each player writes down a word in each category that begins with each of the letters of the key word, the player writing down the most words within a time limit being declared the winner.
5.
Mathematics. a type of mathematical object, as a set, group, or metric space, together with a set of mappings from such an object to other objects of the same type.
[Origin: 1580–90; < LL catégoria < Gk katégoría accusation (also, kind of predication), equiv. to katgor(os) accuser, affirmer (katégor(eǐn) to accuse, affirm, lit., speak publicly against, equiv. to kata-cata-+ -agoreǐn to speak before the agora+ -os n. suffix) + -ia-y3]
A specifically defined division in a system of classification; a class.
A general class of ideas, terms, or things that mark divisions or coordinations within a conceptual scheme, especially:
Aristotle's modes of objective being, such as quality, quantity, or relation, that are inherent in everything.
Kant's modes of subjective understanding, such as singularity, universality, or particularity, that organize perceptions into knowledge.
A basic logical type of philosophical conception in post-Kantian philosophy.
A classificatory structural unit or property of a language, such as a part of speech, verb phrase, or object.
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.
Linguistics
A classificatory structural unit or property of a language, such as a part of speech, verb phrase, or object.
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.
[French catégorie, from Old French, from Late Latin catēgoria, class of predicables, from Greek katēgoriā, accusation, charge, from katēgorein, to accuse, predicate : kat-, kata-, down, against; see cata- + agoreuein, ēgor-, to speak in public (from agorā, marketplace, assembly; see ger- in Indo-European roots).]
1588, from M.Fr. catégorie, from L.L. categoria, from Gk. kategorein "to accuse, assert, predicate," from kata "down to," + agoreuein "to declaim (in the assembly)," from agora "public assembly." Original sense of "accuse" weakened to "assert, name" by the time Aristotle applied kategoria to his 10 classes of things that can be named. Categorical imperative, from the philosophy of Kant, first recorded 1827.
categorytheory A category K is a collection of objects, obj(K), and a collection of morphisms (or "arrows"), mor(K) such that 1. Each morphism f has a "typing" on a pair of objects A, B written f:A->B. This is read 'f is a morphism from A to B'. A is the "source" or "domain" of f and B is its "target" or "co-domain". 2. There is a partial function on morphisms called composition and denoted by an infix ring symbol, o. We may form the "composite" g o f : A -> C if we have g:B->C and f:A->B. 3. This composition is associative: h o (g o f) = (h o g) o f. 4. Each object A has an identity morphism id_A:A->A associated with it. This is the identity under composition, shown by the equations id_B o f = f = f o id_A. In general, the morphisms between two objects need not form a set (to avoid problems with Russell's paradox). An example of a category is the collection of sets where the objects are sets and the morphisms are functions. Sometimes the composition ring is omitted. The use of capitals for objects and lower case letters for morphisms is widespread but not universal. Variables which refer to categories themselves are usually written in a script font. (1997-10-06)
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.
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Audio Help [kat-i-gawr-ee, -gohr-ee] Pronunciation Key 
gor(os) accuser, affirmer (katégor(eǐn) to accuse, affirm, lit., speak publicly against, equiv. to kata- cata- + -agoreǐn to speak before the agora + -os n. suffix) + -ia -y3
