翻訳と辞書 Words near each other ・ MultiCare Health System ・ MultiCare Mary Bridge Children's Hospital & Health Center ・ MultiCare Tacoma General Hospital ・ Multicart ・ Multicast ・ Multicast address ・ Multicast DNS ・ Multicast encryption ・ Multicast lightpaths ・ Multicast Listener Discovery ・ Multicast Open Shortest Path First ・ Multicast router discovery ・ Multicast Routing Daemon v6 ・ Multicast Source Discovery Protocol ・ Multicast-broadcast single-frequency network ・ Multicategory ・ Multicell ・ Multicellular evolution ・ Multicellular organism ・ Multicellular thunderstorm ・ Multicenter AIDS Cohort Study ・ Multicenter Automatic Defibrillator Implantation Trial ・ Multicenter trial ・ Multicentric reticulohistiocytosis ・ Multichannel ・ Multichannel audio ・ Multichannel code ・ Multichannel marketing ・ Multichannel Multipoint Distribution Service ・ Multichannel News Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Multicategory ： ウィキペディア英語版 Multicategory In mathematics (especially category theory), a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a multicategory are analogous to functions of several variables. == Definition == A multicategory consists of * a collection (often a proper class) of ''objects''; * for every finite sequence $(X\_i)\_$ of objects (for von Neumann ordinal $n\; \backslash in\; \backslash mathbb$) and object ''Y'', a set of ''morphisms'' from $(X\_i)\_$ to ''Y''; and * for every object ''X'', a special identity morphism (with ''n'' = 1) from ''X'' to ''X''. Additionally, there are composition operations: Given a sequence of sequences $((X\_)\_)\_$ of objects, a sequence $(Y\_i)\_$ of objects, and an object ''Z'': if * for each $j\; \backslash in\; m$, ''f''''j'' is a morphism from $(X\_)\_$ to ''Y''''j''; and * ''g'' is a morphism from $(Y\_i)\_$ to ''Z'': then there is a composite morphism $g(f\_i)\_$ from $(X\_)\_$ to ''Z''. This must satisfy certain axioms: * If ''m'' = 1, ''Z'' = ''Y''0, and ''g'' is the identity morphism for ''Y''0, then ''g''(''f''0) = ''f''0; * if for each $i\; \backslash in\; m$, ''n''''i'' = 1, $X\_\; =\; Y\_i$, and ''f''''i'' is the identity morphism for ''Y''''i'', then $g(f\_i)\_\; =\; g$; and * an associativity condition: if for each $k\; \backslash in\; m$ and $j\; \backslash in\; n\_k$, $e\_$ is a morphism from $(W\_)\_$, then $g\backslash left(f\_j(e\_)\_\backslash right)\_\; =\; g(f\_i)\_(e\_)\_$ are identical morphisms from $(W\_)\_$ to ''Z''. 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「Multicategory」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.