发表机构
Masaryk University; University of Milan（马萨里克大学; 米兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了编码弱充实的形式范畴论，证明其与拟范畴的无穷宇宙等价，并导出充实版Quillen定理A。
AI 中文摘要
我们以proarrow equipment的形式构造了一种形式范畴论，它编码了在幺半模型范畴$\mV$上的弱相干充实。我们描述了通过该equipment表述的基本范畴概念如何转化回充实范畴。我们将充实范畴的Dwyer-Kan等价刻画为2-范畴等价。特别地，对于单纯集上的Kan-Quillen模型结构或拓扑空间上的Quillen-Serre模型结构，我们证明了所得的形式范畴论等价于与拟范畴的$\infty$-cosmos相关联的形式范畴论，从而将Riehl-Verity意义上的$(\infty,1)$-范畴形式方法扩展到涵盖单纯范畴和拓扑范畴。在$\mV$-范畴的equipment内部表述的分类对象概念，导出了Quillen定理A的充实版本。
英文摘要
A formal category theory is constructed (in the form of a proarrow equipment), encoding weak coherent enrichment over a monoidal model category $\mV$. We describe how basic categorical concepts formulated via the equipment translate back to enriched categories. We characterize Dwyer-Kan equivalences of enriched categories as $2$-categorical equivalences. Specializing to either the Kan-Quillen model structure on simplicial sets, or the Quillen-Serre model structure on topological spaces, we prove that the resulting formal category theory is equivalent to the one associated with the $\infty$-cosmos of quasicategories, thereby extending the formal approach to $(\infty,1)$-categories in the sense of Riehl-Verity to encompass both simplicial and topological categories. A notion of classifying object, formulated internally to the equipment of $\mV$-categories, leads to enriched versions of Quillen's Theorem A.
Commentsadded section 6 on the infinity-equipment; fixed various typos and improved the exposition here and there. remarks and comments are welcome
