论文标题
公制空间和完整性的同位模型
Homotopical models for metric spaces and completeness
论文作者
论文摘要
富含非负实物的相反poset的类别可以看作是公制空间的概括，称为律师公制空间。在本文中，我们在类别上开发了模型结构$ \ MATHBB {r} _+\ text- \ text- \ mathbf {cat} $和$ \ mathbb {r} _+\+\ text- \ text- \ mathbf {cat}}公制空间的研究。更确切地说，在我们构建的三个模型结构中，纤维成型物体是扩展的度量空间（在通常的意义上），Cauchy完整的Lawvere度量标准空间和Cauchy分别完成了扩展的度量空间。最后，我们表明，这些模型结构中的两个与$ \ Mathbf {Cat} $上的规范模型结构相似。
Categories enriched in the opposite poset of non-negative reals can be viewed as generalizations of metric spaces, known as Lawvere metric spaces. In this article, we develop model structures on the categories $\mathbb{R}_+\text-\mathbf{Cat}$ and $\mathbb{R}_+\text-\mathbf{Cat}^{\mathrm{sym}}$ of Lawvere metric spaces and symmetric Lawvere metric spaces, each of which captures different features pertinent to the study of metric spaces. More precisely, in the three model structures we construct, the fibrant-cofibrant objects are the extended metric spaces (in the usual sense), the Cauchy complete Lawvere metric spaces, and the Cauchy complete extended metric spaces, respectively. Finally, we show that two of these model structures are unique in a similar way to the canonical model structure on $\mathbf{Cat}$.
