Movatterモバイル変換

[0]ホーム
URL:

Jump to content
WiktionaryThe Free Dictionary
Search

category

From Wiktionary, the free dictionary
For information about Wiktionary categories, seeWiktionary:Categorization.

English

[edit]
EnglishWikipedia has an article on:
Wikipedia

Etymology

[edit]

LateMiddle English, borrowed fromFrenchcatégorie, fromMiddle Frenchcategorie, fromLate Latincatēgoria(“class of predicables”), fromAncient Greekκατηγορία(katēgoría,“head of predicables”).Doublet ofcategoria.

Pronunciation

[edit]
  • Audio(US):(file)
  • Hyphenation:cat‧e‧go‧ry,cat‧e‧gory

Noun

[edit]

category (pluralcategories)

  1. Agroup, oftennamed ornumbered, to which items areassigned based onsimilarity or definedcriteria.
    Synonyms:class,family,genus,kingdom,order,pigeonhole,phylum,race,tribe,type;see alsoThesaurus:class
    This steep and dangerous climb belongs to the most difficultcategory.
    I wouldn’t put this book in the samecategory as the author’s first novel.
    • 1988, Andrew Radford,Transformational grammar: a first course, Cambridge, UK: Cambridge University Press,→ISBN, page51:
      The traditional way of describing the similarities and differences between constituents is to say that they belong tocategories of various types. Thus, words likeboy,girl,man,woman, etc. are traditionally said to belong to thecategory of Nouns, whereas words likea,the,this, andthat are traditionally said to belong to thecategory of Determiners.
  2. (mathematics) Acollection ofobjects, together with atransitivelyclosedcollection ofcomposablearrows between them, such that every object has anidentity arrow, and such that arrow composition isassociative.
    One well-knowncategory has sets as objects and functions as arrows.
    Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, acategory consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, acategory's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.
    • 1995, Michael Barr with Charles Wells,Category Theory for Computing Science‎[1], 2nd edition, Cambridge, Great Britain: Prentice Hall,§2.8.9, page46:
      The use of the word ‘factor’ shows the explicit intention of categorists to work with functions in an algebraic manner: acategory is an algebra of functions.

Hyponyms

[edit]

Derived terms

[edit]

Related terms

[edit]

Translations

[edit]
group
collection in math

Further reading

[edit]
Retrieved from "https://en.wiktionary.org/w/index.php?title=category&oldid=87305261"
Categories:
Hidden categories:
[8]ページ先頭
©2009-2025 Movatter.jp