Exact categories of topological vector spaces with linear topology
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.
Keywords
Cite
@article{arxiv.2012.15431,
title = {Exact categories of topological vector spaces with linear topology},
author = {Leonid Positselski},
journal= {arXiv preprint arXiv:2012.15431},
year = {2024}
}
Comments
LaTeX 2e with xy-pic; 71 pages, 9 commutative diagrams; v.2: Remark 12.2, Example 13.1(3), and Remark 13.6 inserted; v.3: seven references added; v.4: several misprints corrected, references added and updated, two paragraphs inserted in the Introduction, one in Example 4.1, and one in Section 9; v.5: several misprints corrected