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Meaning of CATEGORY

Pronunciation:  'katu`gowree

 
WordNet Dictionary
 
 Definition: 
  1. [n]  a general concept that marks divisions or coordinations in a conceptual scheme
  2. [n]  a collection of things sharing a common attribute; "there are two classes of detergents"
 

CATEGORY is a 8 letter word that starts with C.

 

 Synonyms: class, family
 
 See Also: accumulation, aggregation, assemblage, class Diplopoda, class Larvacea, class Myriapoda, collection, concept, conception, conjugation, construct, declension, denomination, Diplopoda, form, grammatical category, kind, Larvacea, Malacostraca, Myriapoda, paradigm, pigeonhole, rubric, sex, sort, stamp, subclass Malacostraca, substitution class, superphylum, syntactic category, variety, way

 

 

Webster's 1913 Dictionary
 
 Definition: 
\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.

 
Computing Dictionary
 
 Definition: 

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.

 
Thesaurus Terms
 
 Related Terms: 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
 

 

 

 

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