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Dal'nevostochnyi Matematicheskii Zhurnal, 2023, Volume 23, Number 2, Pages 252–263
DOI: https://doi.org/10.47910/FEMJ202322
(Mi dvmg523)
 

Completeness of the category of separable Chu spaces

V. K. Simakov

Far Eastern Federal University, Vladivostok
References:
Abstract: In this paper we consider the category $\operatorname{Chu}_{Sep}(\mathbf{Set})$ of separable Chu spaces over the category $\mathbf{Set}$ of sets. The construction of the limit of an arbitrary functor into the category of Chu spaces over the category of sets is given when its images on objects are separable Chu spaces. The completeness of the category $\operatorname{Chu}_{Sep}(\mathbf{Set})$ is proved; constructions of equalizers, products and pullbacks in this category are given. It is shown that the colimits of separable Chu spaces are not always separable Chu spaces, but coproducts of separable Chu spaces in the category $\operatorname{Chu}_{Sep}(\mathbf{Set})$ exist for any separable Chu spaces.
Key words: category of Chu spaces, separable Chu spaces, limit, equalizer, product, colimit, coequalizer, coproduct.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-946
The work was carried out at the Far Eastern Center for Mathematical Research with the financial support of the Ministry of Education and Science of Russia, agreement No. 075-02-2023-946 dated February 16, 2023 for the implementation of programs for the development of regional scientific and educational mathematical centers.
Received: 17.03.2023
Accepted: 14.11.2023
Document Type: Article
UDC: 512.58
MSC: Primary 20M30; Secondary 18M05
Language: Russian
Citation: V. K. Simakov, “Completeness of the category of separable Chu spaces”, Dal'nevost. Mat. Zh., 23:2 (2023), 252–263
Citation in format AMSBIB
\Bibitem{Sim23}
\by V.~K.~Simakov
\paper Completeness of the category of separable Chu spaces
\jour Dal'nevost. Mat. Zh.
\yr 2023
\vol 23
\issue 2
\pages 252--263
\mathnet{http://mi.mathnet.ru/dvmg523}
\crossref{https://doi.org/10.47910/FEMJ202322}
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