Sheaves as modules. (English) Zbl 1200.18008
The authors revisit sheaves on locales by placing them in the context of the theory of quantale modules. So they begin, in Section 2, with a description in terms of \(B\)-modules of the open locale maps and obtain direct translations between local homomorphisms and locale modules, early on identifying two isomorphic categories of sheaves as modules, \(B-{\mathcal {LH}}\) and \(B-{\mathcal S}h\), with the same objects.
Reviewer: Dana Piciu (Craiova)
MSC:
| 18F20 | Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) |
| 06D22 | Frames, locales |
| 06F07 | Quantales |
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 18B25 | Topoi |
| 54B40 | Presheaves and sheaves in general topology |
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