EQUIVALENCE OF THE CATEGORY OF PRECUBICAL SETS AND THE CATEGORY OF TRANSITIONAL CHU SPACES WITH PRESERVATION OF THE OPENNESS PROPERTY OF MORPHISMS

E. S. Oshevskaya

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EQUIVALENCE OF THE CATEGORY OF PRECUBICAL SETS AND THE CATEGORY OF TRANSITIONAL CHU SPACES WITH PRESERVATION OF THE OPENNESS PROPERTY OF MORPHISMS

机译：保留形态的开放性的等价子集类别和过渡Chu空间类别的等价性

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摘要

We use directed algebraic topology for establishing categorical relationships between two geometrical models of concurrency, precubical sets and transitional Chu spaces. We study the universal dicovering functor from the category of precubical sets to the category of simply diconnected counterparts of precubical sets. We prove that the category of transitional Chu spaces is equivalent to the category of simply diconnected precubical sets and show that the openness of morphisms is preserved. Bibliography: 19 titles. Illustrations: 7 figures.

机译：我们使用有向代数拓扑在并发，先验集和过渡Chu空间的两个几何模型之间建立分类关系。我们研究了通用发现函子，从子集的类别到子集的简单互联的对应物的类别。我们证明了过渡Chu空间的类别与简单地对立的立方组合的类别相等，并且证明了态射的开放性得以保留。参考书目：19种。插图：7位数字。

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《Journal of Mathematical Sciences》 |2013年第6期|832-850|共19页
作者
E. S. Oshevskaya;
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Sobolev Institute of Mathematics SB RAS 4, pr. Akad. Koptyuga, Novosibirsk 630090, Russia;

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1. Category of Chu spaces over S-Act category [J] . А.А. СТЕПАНОВА, Е.Е.СКУРИХИН, А.Г. СУХОНОС Sibirskie elektronnye matematicheskie izvestiia: Siberian Electronic Mathematical Reports . 2017,第4期

机译：S-Act类别中Chu空间的类别
2. Product of Chu spaces in the category of Chu(S-Act), [J] . Stepanova A. A., Skurihin E. E., Sukhonos A. G. Sibirskie elektronnye matematicheskie izvestiia: Siberian Electronic Mathematical Reports . 2020,第36期

机译：楚（S-ACT）类别中楚空间的产品，
3. Comparing Equivalences on Precubical Sets and Spaces [J] . E. S. Oshevskaya Siberian Advances in Mathematics . 2014,第1期

机译：比较先验集合和空间上的等价关系
4. Morphisms in categories of sets with similarity relations [C] . Jiri Mockor International Fuzzy Systems Association World Congress;European Society of Fuzzy Logic and Technology Conference . 2009

机译：具有相似关系的类别的态度
5. Integrated design for public open space and public art: A set of categories identified and evaluated [D] . Grosset, Christopher James E. 2000

机译：公共开放空间和公共艺术的综合设计：确定和评估的一组类别
6. On Categories of L-Fuzzifying Approximation Spaces L-Fuzzifying Pretopological Spaces and L-Fuzzifying Closure Spaces [O] . Anand Pratap Singh, Irina Perfilieva -1

机译：关于L-模糊化近似空间L-模糊化前拓扑空间和L-模糊化封闭空间的分类
7. A Monoidal Category of Bifinite Chu Spaces [O] . Huang Fang-Ping, Droste Manfred, Zhang Guo-Qiang 2008

机译：双有限楚空间的一个单类别

EQUIVALENCE OF THE CATEGORY OF PRECUBICAL SETS AND THE CATEGORY OF TRANSITIONAL CHU SPACES WITH PRESERVATION OF THE OPENNESS PROPERTY OF MORPHISMS

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