论文标题
Banach空间中丰富的纯度和呈现性
Enriched purity and presentability in Banach spaces
论文作者
论文摘要
Banach空间的类别$禁令和Norm $ \ leq 1 $的线性地图是本地$ \ aleph_1 $ - 可言，但不是本地有限的。但是，我们证明，$ BAN $在完整的度量空间上在丰富的意义上是本地有限的。而且，从这个意义上讲，纯粹的形态只是巴拉克空间的理想。我们表征了大约在具有有限维域和可分离的代码域的形态的集合的Banach空间类别。
The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$-presentable but not locally finitely presentable. We prove, however, that $Ban$ is locally finitely presentable in the enriched sense over complete metric spaces. Moreover, in this sense, pure morphisms are just ideals of Banach spaces. We characterize classes of Banach spaces approximately injective to sets of morphisms having finite-dimensional domains and separable codomains.
