Abstract:A correspondence functor is a functor from the category of finite sets and correspondences to the category of -modules, where is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple modules are projective for the algebra of all relations on a finite set. Moreover, we analyze the occurrence of such simple projective functors inside the correspondence functor  associated with a finite lattice and we deduce a direct sum decomposition of .

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中文翻译：

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简单和射影对应函子

摘要：函函是从有限集和函函的类别到-modules类别的函子，其中是交换环。我们确切地确定哪些简单的函子是射影。我们还确定哪些简单模块对于有限集上所有关系的代数都是投影的。此外，我们分析了与有限晶格相关的对应函子内此类简单射影函子的出现， 并推导了的直接和分解 。

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