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Category 音标拼音: [k'ætəg,ɔri] n. 种类,类项 种类,类项 category 类别 category 种类 范畴 category n 1: a collection of things sharing a common attribute; "there are two classes of detergents" [synonym: {class}, {category}, {family}] 2: a general concept that marks divisions or coordinations in a conceptual scheme Category \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. [1913 Webster] 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. [1913 Webster] 2. Class; also, state, condition, or predicament; as, we are both in the same category. [1913 Webster] There is in modern literature a whole class of writers standing within the same category. --De Quincey. [1913 Webster] 49 Moby Thesaurus words for "category": area, blood, bracket, branch, caste, clan, class, classification, department, division, estate, grade, group, grouping, head, heading, kin, kind, label, league, level, list, listing, order, pigeonhole, position, predicament, race, rank, ranking, rating, rubric, section, sector, sept, set, sort, sphere, station, status, strain, stratum, subdivision, subgroup, suborder, tier, title, type, variety 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)
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