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arXiv · 2012.15431

Exact categories of topological vector spaces with linear topology

Leonid Positselski
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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.

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Leonid Positselski. 2024-05-09. Exact categories of topological vector spaces with linear topology. https://doi.org/10.17323/1609-4514-2024-24-2-219-286

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