论文标题
潜在振动：部分地图类别的纤维
Latent Fibrations: Fibrations for Categories of Partial Maps
论文作者
论文摘要
潜在纤维是一种适应性，适用于通常的纤维化概念的部分图（按限制类别提出）的类别。本文启动了潜在纤维基础理论的发展，并探讨了一些关键例子。潜在振动涵盖了各种各样的示例，其中一些是标准纤维的部分版本，其中一些特定于部分地图类别（尤其是在计算设置中出现的类别）。鉴定出具有各种特殊特性的潜在振动：特别是超连接的潜在纤维可支持纤维化二元的构造；这对于扭转差异编程以及更普遍的镜头理论很重要。
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and explores some key examples. Latent fibrations cover a wide variety of examples, some of which are partial versions of standard fibrations, and some of which are particular to partial map categories (particularly those that arise in computational settings). Latent fibrations with various special properties are identified: hyperconnected latent fibrations, in particular, are shown to support the construction of a fibrational dual; this is important to reverse differential programming and, more generally, in the theory of lenses.
