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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 55

Noncommutative Products on Categories and Chu Construction

Author(s)

Evgeniy E. Skurikhin1,2, Valentin K. Simakov1, Andrey G. Sukhonos1

1 Far Eastern Federal University, Vladivostok, Russian Federation

2 Institute of Applied Mathematics FEB RAS, Vladivostok, Russian Federation

Abstract
The category of Chu spaces is constructed from a given symmetric monoidal closed category 𝐾 and a fixed object in it. If the object is not fixed, we obtain the category 𝐶ℎ𝑢(𝐾), whose objects are Chu spaces and whose morphisms are defined in a more general way. E.E. Skurikhin defined and studied the category of 𝒯 -Chu spaces associated with an arbitrary functor 𝒯 from the product of categories 𝑁 𝑜𝑝 and 𝑀 to the category of sets. In this paper, we prove that if the functor 𝒯 is closed, then the category 𝑀 is isomorphic to a reflective subcategory of the category of 𝒯 -Chu spaces. In the case where the categories 𝑁 and 𝑀 are complete, we present constructions of limits and colimits of arbitrary functors with values in the category of 𝒯 -Chu spaces. We also prove that if 𝐾 is a symmetric monoidal closed category, then 𝐶ℎ𝑢(𝐾) admits the structure of a closed right-monoidal category. As a consequence of the results on 𝒯 -Chu spaces, it follows that the category 𝐶ℎ𝑢(𝐾), as well as the categories of Chu spaces over it, are complete and cocomplete whenever 𝐾 is.
About the Authors

Evgeniy E. Skurikhin, Dr. Sci. (Phys.–Math.), Institute of Applied Mathematics FEB RAS, Vladivostok, 690041, Russian Federation, Far-Eastern Federal University, Vladivostok, 690920, Russian Federation, eeskur@gmail.ru

Valentin K. Simakov, Postgraduate, Far Eastern Federal University, Vladivostok, 690922, Russian Federation, valentin.simakov@yahoo.com

Andrey G. Sukhonos, Cand. Sci. (Phys.-Math.), Assoc. Prof., Far Eastern Federal University, Vladivostok, 690922, Russian Federation, agsukh@mail.ru

For citation
Skurikhin E. E., Simakov V. K., Sukhonos A. G. Noncommutative Products on Categories and Chu Construction. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 55, pp. 144–158. https://doi.org/10.26516/1997-7670.2026.55.144
Keywords
Chu spaces, Chu construction, monoidal category, completeness
UDC
512.58
MSC
18M05
DOI
https://doi.org/10.26516/1997-7670.2026.55.144
References
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