Morita环境下的Eilenberg-Moore范畴和Beck型定理
The Eilenberg-Moore category and a Beck-type theorem for a Morita context
摘要：
描述了单子对的Eilenberg-Moore构造和一个Beck-type定理。更具体地说，一个{ \em森田上下文}的概念，包括两个单子，两个双代数函子和两个连接映射的介绍。结果表明，在许多情况下，代数范畴之间的等价性是由这样的森田上下文诱导的。构造了森田上下文的表征的Eilenberg-Moore范畴。这种构造允许人们将两对伴随函子与具有公共域或{ \em双伴随}的右伴随函子关联到森田上下文。它表明，相反，每一个森田上下文产生的双重附加。定义了双附连中右伴随函子的整环与相应Morita上下文的Eilenberg-Moore范畴之间的比较函子.给出了这一比较函子等价的充必要条件（或一对具有公共定义域的函子的{ \em mortability}）.
英文摘要：
The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a {\em Morita context} comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Morita context is constructed. This construction allows one to associate two pairs of adjoint functors with right adjoint functors having a common domain or a {\em double adjunction} to a Morita context. It is shown that, conversely, every Morita context arises from a double adjunction. The comparison functor between the domain of right adjoint functors in a double adjunction and the Eilenberg-Moore category of the associated Morita context is defined. The sufficient and necessary conditions for this comparison functor to be an equivalence (or for the {\em moritability} of a pair of functors with a common domain) are derived.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
