(厦门理工学院应用数学学院,福建 厦门)

Grothendieck范畴; 斜群范畴; 余极限

Skew Group Categories of Grothendieck Categories
ZHOU Zhenqiang

(School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China)

Grothendieck category; skew group category; colimit

DOI: 10.6043/j.issn.0438-0479.201709008


证明在群阶数|G|可逆的条件下,配备有限群G-作用的Grothendieck范畴C的斜群范畴C(G)是Grothendieck范畴.进一步地,若C还是局部有限生成(局部 Noether或局部有限表现)范畴,则C(G)亦是局部有限生成(局部 Noether或局部有限表现)范畴.

In this article,we prove that the skew group category C(G)of a Grothendieck category C with a finite group G-action is a Grothendieck category,under the condition that the order of the group is invertible in C.Furthermore,if C is a local finitely generated category(local finitely noetherian category or local finitely presented category respectively),then so is C(G).