关于集合的衰落余层
On Faded Cosheaves of Sets
摘要：
证明了在清醒拓扑空间$(B,Ω)$上的Set中的褪色余层范畴等价于一个范畴Sett $(B,Ω)$，它具有与Set $ / B$相同的对象类，但一般具有更宽的态射类.我们还证明了相反的情况：如果$T_0$ -空间$(B,Ω)$上的每一上层同构于$(B,Ω)$中适当映射的管的上层，则$(B,Ω)$是sober的。
英文摘要：
We prove that the category of faded cosheaves in Set over a sober topological space $(B,Ω)$ is equivalent to a category Sett$(B,Ω)$ having the same class of objects as Set$ / B$ has, but generally a wider class of morphisms. We also prove the converse: if each cosheaf over $T_0$-space $(B,Ω)$ is isomorphic to the cosheaf of tubes of an appropriate map ranging in $(B,Ω)$, then $(B,Ω)$ is sober.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
