阿贝尔范畴
在数学中,阿贝尔范畴(或称交换范畴)是一个能对态射与对象取和,而且核与上核存在且满足一定性质的范畴;最基本的例子是阿贝尔群构成的范畴Ab。阿贝尔范畴是同调代数的基本框架。
阿贝尔范畴的公理版本繁多,在此仅取其一(见外部链接)。
一个范畴若满足下述条件,则称阿贝尔范畴:
-
是加法范畴。
- 所有态射皆有核与上核。
- 所有态射皆为严格态射。
只满足前两个条件者称作预阿贝尔范畴。
若取为一交换环,则在上述定义中以k-加法范畴代换加法范畴,便得到k-阿贝尔范畴之定义。
单词 | Abelian category |
释义 |
Abelian category
中文百科
阿贝尔范畴在数学中,阿贝尔范畴(或称交换范畴)是一个能对态射与对象取和,而且核与上核存在且满足一定性质的范畴;最基本的例子是阿贝尔群构成的范畴Ab。阿贝尔范畴是同调代数的基本框架。 阿贝尔范畴的公理版本繁多,在此仅取其一(见外部链接)。 一个范畴
只满足前两个条件者称作预阿贝尔范畴。 若取
英语百科
Abelian category 阿贝尔范畴In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of abelian groups, Ab. The theory originated in an effort to unify several cohomology theories by Alexander Grothendieck and independently in the slightly earlier work of David Buchsbaum. Abelian categories are very stable categories, for example they are regular and they satisfy the snake lemma. The class of Abelian categories is closed under several categorical constructions, for example, the category of chain complexes of an Abelian category, or the category of functors from a small category to an Abelian category are Abelian as well. These stability properties make them inevitable in homological algebra and beyond; the theory has major applications in algebraic geometry, cohomology and pure category theory. Abelian categories are named for Niels Henrik Abel. |
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