翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

discrete category : ウィキペディア英語版
discrete category
In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms:
:hom''C''(''X'', ''X'') = for all objects ''X''
:hom''C''(''X'', ''Y'') = ∅ for all objects ''X'' ≠ ''Y''
Since by axioms, there is always the identity morphism between the same object, we can express the above as condition on the cardinality of the hom-set
:| hom''C''(''X'', ''Y'') | is 1 when ''X'' = ''Y'' and 0 when ''X'' is not equal to ''Y''.
Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category.
== Simple facts ==
Any class of objects defines a discrete category when augmented with identity maps.
Any subcategory of a discrete category is discrete. Also, a category is discrete if and only if all of its subcategories are full.
The limit of any functor from a discrete category into another category is called a product, while the colimit is called a coproduct.
The functor from Set to Cat that sends a set to the corresponding discrete category is left adjoint to the functor sending a small category to its set of objects. (For the right adjoint, see indiscrete category.)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「discrete category」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.