阿贝尔范畴粘合上的有限表现维数

Finitely presented dimensions on recollements of Abelian categories

在阿贝尔范畴中引入了有限表现维数的概念,并讨论了短正合列中对象间有限表现维数的关系。进一步地,令Rab (A,B,C)为阿贝尔范畴粘合,证明了在一定条件下,阿贝尔范畴B的有限表现维数有限当且仅当阿贝尔范畴A与C的有限表现维数有限。

The concepts of finitely presented dimensions in Abelian categories are introduced,and the relations of finitely presented dimensions of objects in a short exact sequence are studied. Let Rab( A,B,C) be a recollement of Abelian categories where A,B and C are abelian categories,it is proved that finitely presented dimension of B is finite if and only if the finitely presented dimensions of A and C are finite under some conditions.