阿贝尔范畴粘合上的表现维数

Presented Dimensions on Recollements of Abelian Categories

在阿贝尔范畴中引入了表现维数的概念,并讨论了短正合列中对象间表现维数的关系.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的表现维数有限,当且仅当阿贝尔范畴A与C的表现维数有限.

The concept of presented dimensions in Abelian categories was introduced and the relations of presented dimensions of objects in a short exact sequence were studied in this paper.Let Rab(A,B,C)be a recollement of Abelian categories where A,B and C are Abelian categories,the presented dimension of B is finite if and only if the presented dimensions of A and C are finite under certain conditions,was proven.