Representation of n-abelian categories in abelian categories

JOURNAL OF ALGEBRA

卷:563

Article

Ebrahimi, Ramin¹  Nasr-Isfahani, Alireza^1,2 

[1] Univ Isfahan, Fac Math & Stat, Dept Pure Math, Esfahan 8174673441, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

关键词: Abelian category;    m-Abelian category;    Embedding theorem;    Homological algebra;    Higher homological algebra;   

DOI  :  10.1016/j.jalgebra.2020.07.010

来源: Elsevier

【 摘 要 】

We prove a higher-dimensional version of the Freyd-Mitchell embedding theorem for n-abelian categories. More precisely, for a positive integer n and a small n-abelian category M, we show that M is equivalent to a full subcategory of an abelian category L-2(M, G), where L-2(M, G) is the category of absolutely pure group valued functors over M. We also show that n-kernels and n-cokernels in M are precisely exact sequences of L-2(M, G) with terms in M. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free