论文标题
内部拆分操作纤维和辅助因子
Internal split opfibrations and cofunctors
论文作者
论文摘要
拆分操作纤维是配备了合适的Opcartesian升降机的函子。本文的目的是通过将适当的升降机选择与这些升降机的特性分开，以表征内部分裂的操作纤维纤维。内部拆分操作纤维的基础结构由配备了内部辅助器的内部函子捕获，而该属性可以表示为回溯条件，类似于内部函子上简单条件是内部离散的OPIBLATION。此外，这种方法通过划分构造和严格的分解系统提供了内部分裂操作纤维纤维的另外特征。对于小类，该理论阐明了计算机科学中出现的三角洲镜头的几个方面。
Split opfibrations are functors equipped with a suitable choice of opcartesian lifts. The purpose of this paper is to characterise internal split opfibrations through separating the structure of a suitable choice of lifts from the property of these lifts being opcartesian. The underlying structure of an internal split opfibration is captured by an internal functor equipped with an internal cofunctor, while the property may be expressed as a pullback condition, akin to the simple condition on an internal functor to be an internal discrete opfibration. Furthermore, this approach provides two additional characterisations of internal split opfibrations, via the décalage construction and strict factorisation systems. For small categories, this theory clarifies several aspects of delta lenses which arise in computer science.
