论文标题
综合类别，测量共同体和富集
Duoidal categories, measuring comonoids and enrichment
论文作者
论文摘要
我们将Sweeder的测量共同体的理论扩展到了综合类别的框架：配备了两个兼容的单体结构的类别。我们使用一种张量产品来赋予另一个类别的类别，并在comonoid类别中富集。富集的霍姆斯由通用测量共同体提供。我们在分级对象和物种的类别以及相关的富集类别上研究了许多综合结构，例如在分级（扭曲的）comonoid中富集分级（扭曲的）单体，以及在对称库拉德群岛中的两个丰富对称性经营。
We extend the theory of Sweeder's measuring comonoids to the framework of duoidal categories: categories equipped with two compatible monoidal structures. We use one of the tensor products to endow the category of monoids for the other with an enrichment in the category of comonoids. The enriched homs are provided by the universal measuring comonoids. We study a number of duoidal structures on categories of graded objects and of species and the associated enriched categories, such as an enrichment of graded (twisted) monoids in graded (twisted) comonoids, as well as two enrichments of symmetric operads in symmetric cooperads.
