论文标题
关系结构类别的扩展
Extensivity of categories of relational structures
论文作者
论文摘要
我们证明，满足温和句法条件的任何关系角理论的模型类别都是无限广泛的。此类类别的中心示例包括预定的集合和部分有序集的类别，以及小$ \ Mathscr {v} $ - 类别 - （对称）伪 - $ \ Mathscr {v} $ - 量子 - 量子空间，（symmetric）$ \ \ \ \ \ \ \ \ Mathscr {v} $ \ mathscr {v} $。我们还明确表征了此类类别的初始来源和最终汇，尤其是嵌入式和商。
We prove that the category of models of any relational Horn theory satisfying a mild syntactic condition is infinitely extensive. Central examples of such categories include the categories of preordered sets and partially ordered sets, and the categories of small $\mathscr{V}$-categories, (symmetric) pseudo-$\mathscr{V}$-metric spaces, and (symmetric) $\mathscr{V}$-metric spaces for a commutative unital quantale $\mathscr{V}$. We also explicitly characterize initial sources and final sinks in such categories, and in particular embeddings and quotients.
