论文标题
度量丰富，有限的一代和小路
Metric enrichment, finite generation, and the path comonad
论文作者
论文摘要
我们证明了许多涉及\ textsc {cmet}的类别的结果，这是具有无限距离的完整度量空间的类别。内在完整度空间的类别\ textsc {cpmet}是本地$ \ aleph_1 $ - 可预见的，封闭的单体和comOnadic，而comonadic comonadic avers \ textsc {cmet}。我们还证明，canvex的类别\ textsc {ccmet}完整的度量空间不是封闭的单体，并且表征等轴测 - $ \ aleph_0 $生成的对象\ textsc {cmet} {cmet}，\ textsc {cpmet}和\ textsc {cpmet} and \ textsc {ccmet} cccmet}，by di libtick。其他结果还包括自动完整性的完整度量的Bi-lipschitz形态，以及这些对（公制空间，Unital $ c^*$ - algebra）的表征，它们在\ textsc {cmet} {cmet}中具有张量的产品 - Unital $ C^*$ - algebras。
We prove a number of results involving categories enriched over \textsc{CMet}, the category of complete metric spaces with possibly infinite distances. The category \textsc{CPMet} of intrinsic complete metric spaces is locally $\aleph_1$-presentable, closed monoidal, and comonadic over \textsc{CMet}. We also prove that the category \textsc{CCMet} of convex complete metric spaces is not closed monoidal and characterize the isometry-$\aleph_0$-generated objects in \textsc{CMet}, \textsc{CPMet} and \textsc{CCMet}, answering questions by Di Liberti and Rosický. Other results include the automatic completeness of a colimit of bi-Lipschitz morphisms of complete metric spaces and a characterization of those pairs (metric space, unital $C^*$-algebra) that have a tensor product in the \textsc{CMet}-enriched category of unital $C^*$-algebras.
