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 quasiabelian. 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.15431
 arXiv:
 arXiv:2012.15431
 Bibcode:
 2020arXiv201215431P
 Keywords:

 Mathematics  Category Theory;
 Mathematics  General Topology
 EPrint:
 LaTeX 2e with xypic