The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transformations. This uses the self-enrichment of the category of abelian groups. If one considers enrichments into symmetric sequences or even bisymmetric sequences, one can produce an endomorphism operad or an endomorphism properad. In this note, we show that more generally, given a category enriched in a monoidal category , the functor that associates to a monoid in its category of representations in is adjoint to the functor that computes the endomorphism monoid of any functor with domain . After describing the first results of the theory we give several examples of applications.

中文翻译：

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表示与内同态伴随

如果人们记得健忘的函子对阿贝尔群的话，则将函子圈到其模块类别的函子具有一个伴随物：线性自然变换的内同态环。这利用了阿贝尔族类别的自我充实。如果一个人考虑将其富集到对称序列甚至双对称序列中，则可以产生一个内同态操作或一个内同构性质。在本注释中，我们表明，更普遍地说，给定一个类别丰富的单曲面类别，与该表示形式的类别中的一个monoid相关联的函子与该函子相邻，该函子可计算任何具有域的函子的内同态monoid。在描述了该理论的最初结果之后，我们给出了几个应用示例。