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Universität Münster（明斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了∞-范畴上分解系统的两个结构性结果：一是对一类∞-范畴纤维化全空间的分解系统分类，二是相关遗忘函子为单子右伴随，丰富了∞-范畴的结构理论。
AI 中文摘要
我们证明了关于∞-范畴上分解系统的两个结构性结果。首先，我们基于基与纤维上的分解系统，对一类∞-范畴纤维化的全空间上的分解系统进行分类，这将通过Juran的双∞-范畴框架解释为配备分解系统的∞-范畴的非/拉直等价；在此过程中，我们发展了通过n重∞-范畴的忠实函子提升的一般理论。其次，我们证明从配备分解系统的∞-范畴到∞-范畴的遗忘函子是单子右伴随。
英文摘要
We prove two structural results about factorization systems on $\infty$-categories. Firstly, we classify factorization systems on the total spaces of a class of fibrations of $\infty$-categories in terms of factorization systems on the base and the fibers. This will be interpreted as an un/straightening equivalence for $\infty$-categories equipped with a factorization system, using Juran's double $\infty$-categorical framework. Along the way, we develop the general theory of lifting through faithful functors of $n$-uple $\infty$-categories. Secondly, we prove that the forgetful functor from $\infty$-categories equipped with a factorization system to $\infty$-categories is a monadic right adjoint.
Comments23 pages
