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Completeness of the category of separable Chu spaces
V. K. Simakov Far Eastern Federal University, Vladivostok
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.
Received: 17.03.2023 Accepted: 14.11.2023
Citation:
V. K. Simakov, “Completeness of the category of separable Chu spaces”, Dal'nevost. Mat. Zh., 23:2 (2023), 252–263
Linking options:
https://www.mathnet.ru/eng/dvmg523 https://www.mathnet.ru/eng/dvmg/v23/i2/p252
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Abstract page: | 57 | Full-text PDF : | 19 | References: | 13 |
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