The Brauer Group of Central Separable Monoids in a Braided Monoidal Category

• 来源期刊: 代数集刊（英文版）
• 关键词: braided monoidal category separable monoids central monoids Azumaya monoids Brauer groups
• 年，卷（期）: 2002,（4）
• 页码范围: 399-416
• 页数: 18页
• 语种: 英文

摘要

For a braided monoidal category (C,(○×), K, c), in a previous paper, we construct a Brauer group B1,c(C) for the 1-Azumaya monoids in C. In this paper,we investigate separability and centrality properties for 1-Azumaya monoids when the coequalizers in C are stable. This leads to the notion of 2-Azumaya monoids,and to a new subgroup B2,c(C) of the Brauer group B1,c(C) that generalizes the analogous groups in the symmetric case. Finally, we prove that B2,c(C) and B1,c(C) are equal if the base object of the category is projective.