正合范畴与广义Abel范畴中的正合性引理  

Lemmas on exactness in exact categories and in generalized Abelian categories

作　　者：荣石 章璞 Shi Rong;Pu Zhang

机构地区：[1]上海交通大学数学科学学院,上海200240

出　　处：《中国科学：数学》2021年第10期1655-1676,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11971304)资助项目。

摘　　要：弱幂等完备正合范畴和广义Abel范畴是Abel范畴两种重要的推广.蛇引理是同调代数中最基本的引理.本文指出在弱幂等完备正合范畴中,三种形式的蛇引理、同调代数基本定理和3×3引理这五条定理都成立,并且互相等价,由此可推导出其他正合性引理.在广义Abel范畴中,三种形式的蛇引理都成立,并且互相等价,由此可推导出同调代数基本定理和其他正合性引理.Weakly idempotent complete exact categories and generalized Abelian categories are two important generalizations of Abelian categories. Snake lemma is one of the most fundamental lemmas in homological algebra.In this paper, we point out that the three forms of Snake lemma, the fundamental theorem of homological algebra,and the 3 × 3 lemma, are true and equivalent, in the weakly idempotent complete exact categories;and they imply other lemmas on exactness. In generalized Abelian categories, the three forms of Snake lemma are true and equivalent;and they imply the fundamental theorem of homological algebra and other lemmas on exactness.

关 键 词：弱幂等完备正合范畴 广义Abel范畴 正合性 蛇引理 同调代数基本定理 3×3引理 

分 类 号：O154.1[理学—数学]