翻訳と辞書 Words near each other ・ Quasiperfect number ・ Quasiperiodic function ・ Quasiperiodic motion ・ Quasiperiodic tiling ・ Quasiperiodicity ・ Quasipetalichthyidae ・ Quasipetalichthys ・ Quasiprobability distribution ・ Quasiregular ・ Quasiregular element ・ Quasiregular map ・ Quasiregular polyhedron ・ Quasiregular representation ・ Quasireversibility ・ Quasi-birth–death process ・ Quasi-category ・ Quasi-commutative property ・ Quasi-compact morphism ・ Quasi-constitutionality ・ Quasi-continuous function ・ Quasi-contract ・ Quasi-criminal ・ Quasi-crystals (supramolecular) ・ Quasi-delict ・ Quasi-derivative ・ Quasi-elemental ・ Quasi-empirical method ・ Quasi-empiricism in mathematics ・ Quasi-experiment ・ Quasi-fibration 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 Quasi-category ： ウィキペディア英語版 Quasi-category In mathematics, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category. The study of such generalizations is known as higher category theory. Quasi-categories were introduced by . André Joyal has much advanced the study of quasi-categories showing that most of the usual basic category theory and some of the advanced notions and theorems have their analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories has been expounded by . Quasi-categories are certain simplicial sets. Like ordinary categories, they contain objects (the 0-simplices of the simplicial set) and morphisms between these objects (1-simplices). But unlike categories, the composition of two morphisms need not be uniquely defined. All the morphisms that can serve as composition of two given morphisms are related to each other by higher order invertible morphisms (2-simplices thought of as "homotopies"). These higher order morphisms can also be composed, but again the composition is well-defined only up to even higher order invertible morphisms, etc. The idea of higher category theory (at least, higher category theory when higher morphisms are invertible) is that, as opposed to the standard notion of a category, there should be a mapping space (rather than a mapping set) between two objects. This suggests that a higher category should simply be a topologically enriched category. The model of quasi-categories is, however, better suited to applications than that of topologically enriched categories, though it has been proved by Lurie that the two have natural model structures that are Quillen equivalent. ==Definition== By definition, a quasi-category ''C'' is a simplicial set satisfying the inner Kan conditions (also called weak Kan condition): every inner horn in ''C'', namely a map of simplicial sets $\backslash Lambda^k()\backslash to\; C$ where The idea is that 2-simplices $\backslash Delta()\; \backslash to\; C$ are supposed to represent commutative triangles (at least up to homotopy). A map $\backslash Lambda^1()\; \backslash to\; C$ represents a composable pair. Thus, in a quasi-category, one cannot define a composition law on morphisms, since one can choose many ways to compose maps. One consequence of the definition is that $C^\; \backslash to\; C^$ is a trivial Kan fibration. In other words, while the composition law is not uniquely defined, it is unique up to a contractible choice. 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「Quasi-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.