论文标题
笛卡尔分解系统和Grothendieck纤维
Cartesian Factorization Systems and Grothendieck Fibrations
论文作者
论文摘要
每个Grothendieck纤维都会引起其域上的垂直/笛卡尔正交分解系统。我们将笛卡尔分解系统定义为正交分解，其中左等级满足2中的2中，并在沿右类回调下关闭。我们努力表明，该定义抽象了与Grothendieck振动相关的垂直/笛卡尔分解系统的关键特征，并在各种2类分解系统和Grothendieck纤维之间进行比较，以证明这种关系。然后，我们给出一种与笛卡尔分解系统水平上的振动相反的纤维相反的结构。 除了最终的双重分类结果外，本文完全回顾了先前建立的材料。它应读为说明性注释。
Every Grothendieck fibration gives rise to a vertical/cartesian orthogonal factorization system on its domain. We define a cartesian factorization system to be an orthogonal factorization in which the left class satisfies 2-of-3 and is closed under pullback along the right class. We endeavor to show that this definition abstracts crucial features of the vertical/cartesian factorization system associated to a Grothendieck fibration, and give comparisons between various 2-categories of factorization systems and Grothendieck fibrations to demonstrate this relationship. We then give a construction which corresponds to the fiberwise opposite of a Grothendieck fibration on the level of cartesian factorization systems. Apart from the final double categorical results, this paper is entirely review of previously established material. It should be read as an expository note.
