Exact categories of topological vector spaces with linear topology

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00585952" target="_blank" >RIV/67985840:_____/24:00585952 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.17323/1609-4514-2024-24-2-219-286" target="_blank" >https://doi.org/10.17323/1609-4514-2024-24-2-219-286</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.17323/1609-4514-2024-24-2-219-286" target="_blank" >10.17323/1609-4514-2024-24-2-219-286</a>

Result language
angličtina
Original language name
Exact categories of topological vector spaces with linear topology
Original language description
We explain why the naïve definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to Beilinson’s paper 'Remarks on topological algebras' (Moscow Mathematical Journal 8:1 (2008), 1–20), 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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