Noncommutative Topologies,Localization, and Sheaves |
| |
| Authors: | Judit Mendoza Aguilar Alain Verschoren |
| |
| Affiliation: | 1. Department of Fundamental Mathematics , University of La Laguna , La Laguna, Canary Islands, Spain;2. Department of Mathematics and Computer Science , University of Antwerp , Antwerp, Belgium |
| |
| Abstract: | In this note, we introduce and study the notion of sheaf on a noncommutative topology and construct an associated sheafification functor in this noncommutative context. It appears that abstract localization in the category of presheaves on a partially ordered set provides an elegant way to define this sheafification functor, generalizing similar constructions in the commutative case. |
| |
| Keywords: | Noncommutative topologies Quantales Sheaves |
|
|
