2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77992We 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.AMS-LaTeX, 3 pages, corrected abstractGeneral TopologyCategory Theory54B40 (Primary) 18B99 (Secondary)text