category

category
    n 1: a collection of things sharing a common attribute; "there
         are two classes of detergents" [syn: {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]
    

category

   <theory> 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)
    

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