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Categorical Properties of Soft Sets
The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the category SFun of soft sets and soft functions has equalizers, finite products, pullbac...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi Publishing Corporation
2014
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4157215/ https://www.ncbi.nlm.nih.gov/pubmed/25215333 http://dx.doi.org/10.1155/2014/783056 |
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author | Zhou, Min Li, Shenggang Akram, Muhammad |
author_facet | Zhou, Min Li, Shenggang Akram, Muhammad |
author_sort | Zhou, Min |
collection | PubMed |
description | The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the category SFun of soft sets and soft functions has equalizers, finite products, pullbacks, and exponential properties. It is worth mentioning that we find that SFun is both a topological construct and Cartesian closed. The category SRel of soft sets and Z-soft set relations is also characterized, which shows the existence of the zero objects, biproducts, additive identities, injective objects, projective objects, injective hulls, and projective covers. Finally, by constructing proper adjoint situations, some intrinsic connections between SFun and SRel are established. |
format | Online Article Text |
id | pubmed-4157215 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
spelling | pubmed-41572152014-09-11 Categorical Properties of Soft Sets Zhou, Min Li, Shenggang Akram, Muhammad ScientificWorldJournal Research Article The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the category SFun of soft sets and soft functions has equalizers, finite products, pullbacks, and exponential properties. It is worth mentioning that we find that SFun is both a topological construct and Cartesian closed. The category SRel of soft sets and Z-soft set relations is also characterized, which shows the existence of the zero objects, biproducts, additive identities, injective objects, projective objects, injective hulls, and projective covers. Finally, by constructing proper adjoint situations, some intrinsic connections between SFun and SRel are established. Hindawi Publishing Corporation 2014 2014-08-18 /pmc/articles/PMC4157215/ /pubmed/25215333 http://dx.doi.org/10.1155/2014/783056 Text en Copyright © 2014 Min Zhou et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Zhou, Min Li, Shenggang Akram, Muhammad Categorical Properties of Soft Sets |
title | Categorical Properties of Soft Sets |
title_full | Categorical Properties of Soft Sets |
title_fullStr | Categorical Properties of Soft Sets |
title_full_unstemmed | Categorical Properties of Soft Sets |
title_short | Categorical Properties of Soft Sets |
title_sort | categorical properties of soft sets |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4157215/ https://www.ncbi.nlm.nih.gov/pubmed/25215333 http://dx.doi.org/10.1155/2014/783056 |
work_keys_str_mv | AT zhoumin categoricalpropertiesofsoftsets AT lishenggang categoricalpropertiesofsoftsets AT akrammuhammad categoricalpropertiesofsoftsets |