翻訳と辞書
Words near each other
・ Free Judges
・ Free jumping
・ Free Kamal
・ Free kick
・ Free kick (Australian rules football)
・ Free kick (rugby union)
・ Free Kick Masters
・ Free Kirk
・ Free Kitten
・ Free Knowledge Foundation
・ Free Knowledge Institute
・ Free Lancing
・ Free Land
・ Free Land (film)
・ Free laptop distribution scheme of the Uttar Pradesh government
Free lattice
・ Free Lebanon State
・ Free Legal Advice Centres
・ Free Legal Assistance Group
・ Free Library
・ Free Library and Reading Room-Williamstown Memorial Library
・ Free Library of Philadelphia
・ Free Library of Springfield Township
・ Free Libyan Air Force
・ Free Libyana
・ Free license
・ Free license (disambiguation)
・ Free Lie algebra
・ Free Life (album)
・ Free Life (balloon)


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

Free lattice : ウィキペディア英語版
Free lattice
In mathematics, in the area of order theory, a free lattice is the free object corresponding to a lattice. As free objects, they have the universal property.
==Formal definition==
Any set ''X'' may be used to generate the free semilattice ''FX''. The free semilattice is defined to consist of all of the finite subsets of ''X'', with the semilattice operation given by ordinary set union. The free semilattice has the universal property. The universal morphism is (''FX'',η), where η is the unit map η:''X''→''FX'' which takes ''x''∈''X'' to the singleton set . The universal property is then as follows: given any map ''f'':''X''→''L'' from ''X'' to some arbitrary semilattice ''L'', there exists a unique semilattice homomorphism \tilde:FX\to L such that f=\tilde\circ\eta. The map \tilde may be explicitly written down; it is given by
:S\in FX \mapsto\bigvee\left\
Here, \bigvee denotes the semilattice operation in ''L''. This construction may be promoted from semilattices to lattices; by construction the map \tilde will have the same properties as the lattice.
The symbol ''F'' is then a functor from the category of sets to the category of lattices and lattice homomorphisms. The functor ''F'' is left adjoint to the forgetful functor from lattices to their underlying sets. The free lattice is a free object.

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「Free lattice」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.