论文标题
可访问类别理论中的虚拟概念
Virtual concepts in the theory of accessible categories
论文作者
论文摘要
我们通过引入两个新的虚拟反射率和虚拟正交性的新概念来提供丰富的可访问类别的新表征，以此作为对本地呈现类别的常规反射率和正交条件的概括。虚拟词是指在较小的限制下涉及的$ \ MATHCAL V $ - 类别的免费完成时给出的反射率和正交条件，而不是$ \ Mathcal V $ -Stategory本身。通过这种方式，我们希望对理论提供更清晰的理解，以及一种识别可访问$ \ Mathcal V $类别的有用方式。在最后一部分中，我们证明了2类可访问的$ \ Mathcal V $ - 类别，可访问的$ \ Mathcal V $ - functors和$ \ Mathcal V $ - 自然转换都具有灵活的限制。
We provide a new characterization of enriched accessible categories by introducing the two new notions of virtual reflectivity and virtual orthogonality as a generalization of the usual reflectivity and orthogonality conditions for locally presentable categories. The word virtual refers to the fact that the reflectivity and orthogonality conditions are given in the free completion of the $\mathcal V$-category involved under small limits, instead of the $\mathcal V$-category itself. In this way we hope to provide a clearer understanding of the theory as well as a useful way of recognizing accessible $\mathcal V$-categories. In the last section we prove that the 2-category of accessible $\mathcal V$-categories, accessible $\mathcal V$-functors, and $\mathcal V$-natural transformations has all flexible limits.
