论文标题
Burroni T-功能的全面分解
The comprehensive factorization of Burroni's T-functors
论文作者
论文摘要
在C上的单个t条件下，我们确定即使在Burroni的（内部）t类别及其函子的Burroni类别CAT（T）中也存在这种正交分解系统的全面分解。此上下文提供了一些预期的应用程序和一些意外的连接。例如，它使我们能够推断出兰贝克多兼仪的功能因子也可以进行全面的分解。在拓扑结构中，它导致了一个见解，即离散联合启动的作用是通过完美的地图扮演的，并通过其纤维方向的紧凑型给出了连续图的全面分解。
Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal) T-categories and their functors. This context provides for some expected applications and some unexpected connections. For example, it lets us deduce that the comprehensive factorization is also available for functors of Lambek's multicategories. In topology, it leads to the insight that the role of discrete cofibrations is played by perfect maps, with the comprehensive factorization of a continuous map given by its fibrewise compactification.
