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Mathematics > Category Theory
Title: Exact categories of topological vector spaces with linear topology
(Submitted on 31 Dec 2020 (v1), last revised 9 May 2024 (this version, v5))
Abstract: 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.
Submission history
From: Leonid Positselski [view email][v1] Thu, 31 Dec 2020 03:52:40 GMT (59kb)
[v2] Mon, 4 Jan 2021 23:03:54 GMT (60kb)
[v3] Tue, 9 Mar 2021 20:39:28 GMT (61kb)
[v4] Tue, 26 Sep 2023 09:43:12 GMT (62kb)
[v5] Thu, 9 May 2024 15:13:50 GMT (62kb)
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