On Faded Cosheaves of Sets

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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.
AMS-LaTeX, 3 pages, corrected abstract

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General Topology, Category Theory, 54B40 (Primary) 18B99 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77992

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9901103
 http://arxiv.org/abs/math/9901103

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arXiv