论文标题
具有一系列限制的可访问类别
Accessible categories with a class of limits
论文作者
论文摘要
在本文中，我们表征了具有指定类限制的那些可访问的$ \ Mathcal V $ - 类别。我们通过介绍一类权重$ψ$的伴侣$ \ mathfrak c $的概念来做到这一点，作为与$ψ$兼容的特殊类型的colimit图的集合。然后，我们将带有$ψ$限制的可访问的$ \ Mathcal V $ - 类别描述为那些可访问的嵌入方式和$ \ Mathfrak c $ -virtally在presheaf $ \ Mathcal v $ -category中反射，作为$ \ Mathcal v $ of $ \ Mathfrak c $ c $ c $ - mmathfrak c $ - mmathfrak c $ - mmather-cation。这使我们能够恢复标准定理，以作为本地可呈现的，可局部多重和本地多种概述的类别作为同一一般框架的实例。此外，我们的定理涵盖了任何弱声音类别$ψ$的情况，并就本地可呈现的类别的情况提供了新的观点。
In this paper we characterize those accessible $\mathcal V$-categories that have limits of a specified class. We do this by introducing the notion of companion $\mathfrak C$ for a class of weights $Ψ$, as a collection of special types of colimit diagrams that are compatible with $Ψ$. We then characterize the accessible $\mathcal V$-categories with $Ψ$-limits as those accessibly embedded and $\mathfrak C$-virtually reflective in a presheaf $\mathcal V$-category, and as the $\mathcal V$-categories of $\mathfrak C$-models of sketches. This allows us to recover the standard theorems for locally presentable, locally multipresentable, and locally polypresentable categories as instances of the same general framework. In addition, our theorem covers the case of any weakly sound class $Ψ$, and provides a new perspective on the case of weakly locally presentable categories.
