Yoneda lemma for enriched infinity categories
Yoneda lemma for enriched infinity categories
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丰富无穷范畴的米田引理
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发表时间：
2018
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通讯作者：
V. Hinich
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作者：
V. Hinich
我们继续研究丰富的无穷范畴，使用的定义相当于Gepner和Haugseng。在我们的方法中，丰富的无穷范畴是一个特别设计的丰富箭图的monoidal范畴中的联想monoids。证明了当基本范畴M中的么半群结构来自直积时，我们的定义与通过Segal对象的方法本质等价。此外，我们将我们的概念与M上的范畴左张量概念进行比较，并在此背景下证明了Yoneda引理的一个版本。
版本2：更正了2.6.2中的错误。
版本3：一些小的更正。
版本4：增加了第8节，描述了丰富类别的对应关系。当基本么半群范畴M是一个具有Carnival结构的Prototopos时，我们证明了对应范畴等价于[1]上的丰富范畴范畴.
第5版：更改了术语（以前的bicartesian fibrations变为bibrations），纠正了一些印刷错误。
版本6：增加了第2.11节，涉及操作筛。根据裁判的要求进行了一些更正和澄清。
版本7：最终版本，接受数学进步。
We continue the study of enriched infinity categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched infinity categories are associative monoids in an especially designed monoidal category of enriched quivers. We prove that, in case the monoidal structure in the basic category M comes from 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.
Version 2: An error in 2.6.2 corrected.
Version 3: a few minor corrections.
Version 4: Section 8 added, describing correspondences of enriched categories. In case the basic monoidal category M is a prototopos with a cartesian structure, we prove that the category of correspondences is equivalent to the category of enriched categories over [1].
Version 5: terminology changed (former bicartesian fibrations became bifibrations), a few misprints corrected.
Version 6: Section 2.11 added, dealing with operadic sieves. A number of corrections and clarifications made per referee's request.
Version 7: final version, accepted to Advances in Math.