内射森田上下文（重访）
Injective Morita contexts (revisited)
摘要：
本文讨论了所谓的内射Morita上下文（其中连接双模态射是内射的）和Morita $α$上下文（其中连接双模在Zimmermann-Huisgen意义下具有局部投射性）.在只有一个迹理想起作用或双模态射之间不需要相容性的情况下，我们引入了Morita半上下文和Morita数据的概念，并对它们进行了研究.内射森田数据将被用来（在静态和adstatic模块的帮助下）建立一些相交的子范畴之间的等价关系，这些子范畴与由森田数据的迹理想局部化或共局部化的模块的子范畴有关。最后我们将$α$ -context应用于$\ast$ -模和内射右宽Morita context.
英文摘要：
This paper is an exposition of the so-called injective Morita contexts (in which the connecting bimodule morphisms are injective) and Morita $α$contexts (in which the connecting bimodules enjoy some local projectivity in the sense of Zimmermann-Huisgen). Motivated by situations in which only one trace ideal is in action, or the compatibility between the bimodule morphisms is not needed, we introduce the notions of Morita semi-contexts and Morita data, and investigate them. Injective Morita data will be used (with the help of static and adstatic modules) to establish equivalences between some intersecting subcategories related to subcategories of modules that are localized or colocalized by trace ideals of a Morita datum. We end up with applications of Morita $α$-contexts to $\ast$-modules and injective right wide Morita contexts.
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