Noncommutative topologies, localization, and sheaves. (English) Zbl 1144.18010
Summary: 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.
MSC:
| 18F20 | Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) |
| 06F07 | Quantales |
| 14A22 | Noncommutative algebraic geometry |
| 54B40 | Presheaves and sheaves in general topology |
References:
| [1] | DOI: 10.1007/BF00403411 · Zbl 0595.18003 · doi:10.1007/BF00403411 |
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