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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...

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Detalles Bibliográficos
Autores principales: Zhou, Min, Li, Shenggang, Akram, Muhammad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
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.
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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
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