阿贝尔范畴粘合上的表现维数
Presented Dimensions on Recollements of Abelian Categories
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摘要: 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(\mathscrA,\mathscrB, \mathscrC)为阿贝尔范畴粘合,证明了在一定条件下,阿贝尔范畴\mathscrB的表现维数有限,当且仅当阿贝尔范畴\mathscrA与\mathscrC的表现维数有限.Abstract: 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(\mathscrA, \mathscrB, \mathscrC) be a recollement of Abelian categories where \mathscrA, \mathscrB and \mathscrC are Abelian categories, the presented dimension of \mathscrB is finite if and only if the presented dimensions of \mathscrA and \mathscrC are finite under certain conditions, was proven.