理解范畴的自由构造
Free constructions for comprehension categories
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中文总结 AI 辅助
该研究探究理解范畴与劳沃尔-埃尔哈德理解范畴的关系，完成从纤维化构造自由理解范畴、从雅各布斯理解范畴构造自由劳沃尔-埃尔哈德理解范畴的工作。
中文摘要 AI 辅助
雅各布斯（Jacobs）理解范畴涵盖了大量类型依赖的范畴模型，也支持描述类型之间的态射。我们研究理解范畴与一类特定子类（称为劳沃尔-埃尔哈德（Lawvere-Ehrhard）理解范畴）的关系：首先通过比较给定理解范畴关联的项纤维化与类型态射纤维化来刻画该子类；其次给出从纤维化构造自由理解范畴的方法；最后从雅各布斯理解范畴构造自由劳沃尔-埃尔哈德理解范畴。
英文摘要
Jacobs comprehension categories subsume a large class of categorical models of type dependency, supporting also the description of morphisms between types. We study the relationship between comprehension categories and a particular subclass, which we call Lawvere-Ehrhard comprehension categories. First, we characterize this subclass by comparing a fibration of terms and a fibration of type morphisms associated to a given comprehension category. Next, we provide the construction of the free comprehension category over a fibration. Finally, we construct the free Lawvere-Ehrhard comprehension category over a Jacobs comprehension category.
