Cubical Sets and Trace Monoid Actions
This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and t...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/285071 |
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| _version_ | 1832562874560544768 |
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| author | Ahmet A. Husainov |
| author_facet | Ahmet A. Husainov |
| author_sort | Ahmet A. Husainov |
| collection | DOAJ |
| description | This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and trace monoid actions are constructed. These functors carry independence preserving morphisms in the independence preserving morphisms. This allows us to build adjoint functors between the category of weak asynchronous systems and the category of higher dimensional automata. |
| format | Article |
| id | doaj-art-6556fad14bf546e199f0a2177ae182a7 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-6556fad14bf546e199f0a2177ae182a72025-02-03T01:21:29ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/285071285071Cubical Sets and Trace Monoid ActionsAhmet A. Husainov0Faculty of Computer Technology, Komsomolsk-on-Amur State Technical University, Prospect Lenina 27, Komsomolsk-on-Amur 681013, RussiaThis paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and trace monoid actions are constructed. These functors carry independence preserving morphisms in the independence preserving morphisms. This allows us to build adjoint functors between the category of weak asynchronous systems and the category of higher dimensional automata.http://dx.doi.org/10.1155/2013/285071 |
| spellingShingle | Ahmet A. Husainov Cubical Sets and Trace Monoid Actions The Scientific World Journal |
| title | Cubical Sets and Trace Monoid Actions |
| title_full | Cubical Sets and Trace Monoid Actions |
| title_fullStr | Cubical Sets and Trace Monoid Actions |
| title_full_unstemmed | Cubical Sets and Trace Monoid Actions |
| title_short | Cubical Sets and Trace Monoid Actions |
| title_sort | cubical sets and trace monoid actions |
| url | http://dx.doi.org/10.1155/2013/285071 |
| work_keys_str_mv | AT ahmetahusainov cubicalsetsandtracemonoidactions |