Symmetric monoidal categories of conveniently-constructible Banach bundles
| Autor: | Chirvasitu, Alexandru |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that a continuously-normed Banach bundle $\mathcal{E}$ over a compact Hausdorff space $X$ whose space of sections is algebraically finitely-generated (f.g.) over $C(X)$ is locally trivial (and hence the section space is projective f.g over $C(X)$); this answers a question of I. Gogi\'c. As a preliminary we also provide sufficient conditions for a quotient bundle to be continuous phrased in terms of the Vietoris continuity of the unit-ball maps attached to the bundles. Related results include (a) the fact that the category of topologically f.g. continuous Banach bundles over $X$ is symmetric monoidal under the (fiber-wise-maximal) tensor product, (b) the full faithfulness of the global-section functor from topologically f.g. continuous bundles to $C(X)$-modules and (c) the consequent identification of the algebraically f.g. bundles as precisely the rigid objects in the aforementioned symmetric monoidal category. Comment: 22 pages + references; v2 corrects typos and makes small style changes |
| Databáze: | arXiv |
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