Exact categories of topological vector spaces with linear topology
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911877274009600 |
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| author | Positselski, Leonid |
| author_facet | Positselski, Leonid |
| contents | We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to arXiv:0711.2527, the category of such topological vector spaces is not quasi-abelian. We present a corrected definition of exact category structure which works OK. Then we explain that the corrected definition still has a shortcoming in that a natural tensor product functor is not exact in it, and discuss ways to refine the exact category structure so as to make the tensor product functors exact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_15431 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Exact categories of topological vector spaces with linear topology Positselski, Leonid Category Theory General Topology We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to arXiv:0711.2527, the category of such topological vector spaces is not quasi-abelian. We present a corrected definition of exact category structure which works OK. Then we explain that the corrected definition still has a shortcoming in that a natural tensor product functor is not exact in it, and discuss ways to refine the exact category structure so as to make the tensor product functors exact. |
| title | Exact categories of topological vector spaces with linear topology |
| topic | Category Theory General Topology |
| url | https://arxiv.org/abs/2012.15431 |