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category

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category


  3  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  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. 
 
  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. 
 
  From  WordNet  r  1.6  [wn]: 
 
  category 
  n  1:  a  collection  of  things  sharing  a  common  attribute;  "there 
  are  two  classes  of  detergents"  [syn:  {class},  {family}] 
  2:  a  general  concept  that  marks  divisions  or  coordinations  in  a 
  conceptual  scheme 
 
  From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]: 
 
  category 
 
    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) 
 
 




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