| 翻訳と辞書 |
| triangulated category ： ウィキペディア英語版 |
triangulated category
In mathematics, a triangulated category is a category together with additional structure, a "translation functor" and a class of "distinguished triangles". Prominent examples are the derived category of an abelian category (more generally, the homotopy category of a stable ∞-category) and the stable homotopy category of spectra, both of which carry the structure of a triangulated category in a natural fashion. The distinguished triangles are reminiscent of the long exact sequences of homology; they play a role akin to that of short exact sequences in abelian categories.
A t-category is a triangulated category with a t-structure.
== History ==
The notion of a derived category was introduced by in his Ph.D. thesis, based on the ideas of Grothendieck. He also defined the notion of a triangulated category, based upon the observation that a derived category had some special "triangles", by writing down axioms for the basic properties of these triangles. A very similar set of axioms was written down at about the same time by .
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「triangulated 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.
|
|