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Yoneda lemma for enriched ∞-categories
Advances in Mathematics ( IF 1.5 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.aim.2020.107129
Vladimir Hinich

Abstract We continue the study of enriched ∞-categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched ∞-categories are associative monoids in an especially designed monoidal category of enriched quivers. We prove that, in the case where the monoidal structure in the basic category M comes from the direct product, our definition is essentially equivalent to the approach via Segal objects. Furthermore, we compare our notion with the notion of category left-tensored over M , and prove a version of Yoneda lemma in this context. We apply the Yoneda lemma to the study of correspondences of enriched (for instance, higher) ∞-categories.

中文翻译:

丰富的 ∞ 类别的 Yoneda 引理

摘要 我们使用与 Gepner 和 Haugseng 的定义等效的定义继续研究丰富的 ∞ 类别。在我们的方法中,丰富的 ∞ 类别是特别设计的丰富箭袋的幺半群中的关联幺半群。我们证明,在基本范畴 M 中的幺半群结构来自直积的情况下,我们的定义本质上等同于通过 Segal 对象的方法。此外,我们将我们的概念与 M 上的左张量范畴的概念进行比较,并在这种情况下证明了米田引理的一个版本。我们将米田引理应用于研究丰富的(例如,更高的)∞ 类别的对应关系。
更新日期:2020-06-01
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