A simplification functor for coalgebras
For an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the canonical projections onto the simple factor split, generalizes the well-known notion of simple coalgebras. In case F weakly preserves kernels, the passage from a coalgebra to its simple factor is func...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/56786 |
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| _version_ | 1832545567510626304 |
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| author | Maurice Kianpi Celestin Nkuimi Jugnia |
| author_facet | Maurice Kianpi Celestin Nkuimi Jugnia |
| author_sort | Maurice Kianpi |
| collection | DOAJ |
| description | For an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the canonical projections onto the simple factor split, generalizes the well-known notion of
simple coalgebras. In case F weakly preserves kernels, the passage from a coalgebra to its simple factor is functorial. This is the simplification functor. It is left adjoint to the
inclusion of the subcategory of simple coalgebras into the category SetF of F-coalgebras, making it an epireflective one. If a product of split coalgebras exists, then this is split and preserved by the simplification functor. In
particular, if a product of simple coalgebras exists, this is simple too. |
| format | Article |
| id | doaj-art-3f63d8795d1d4450a870671ade9a29d0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3f63d8795d1d4450a870671ade9a29d02025-02-03T07:25:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/5678656786A simplification functor for coalgebrasMaurice Kianpi0Celestin Nkuimi Jugnia1Laboratory of Algebra, Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812, Yaounde, CameroonLaboratory of Algebra, Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812, Yaounde, CameroonFor an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the canonical projections onto the simple factor split, generalizes the well-known notion of simple coalgebras. In case F weakly preserves kernels, the passage from a coalgebra to its simple factor is functorial. This is the simplification functor. It is left adjoint to the inclusion of the subcategory of simple coalgebras into the category SetF of F-coalgebras, making it an epireflective one. If a product of split coalgebras exists, then this is split and preserved by the simplification functor. In particular, if a product of simple coalgebras exists, this is simple too.http://dx.doi.org/10.1155/IJMMS/2006/56786 |
| spellingShingle | Maurice Kianpi Celestin Nkuimi Jugnia A simplification functor for coalgebras International Journal of Mathematics and Mathematical Sciences |
| title | A simplification functor for coalgebras |
| title_full | A simplification functor for coalgebras |
| title_fullStr | A simplification functor for coalgebras |
| title_full_unstemmed | A simplification functor for coalgebras |
| title_short | A simplification functor for coalgebras |
| title_sort | simplification functor for coalgebras |
| url | http://dx.doi.org/10.1155/IJMMS/2006/56786 |
| work_keys_str_mv | AT mauricekianpi asimplificationfunctorforcoalgebras AT celestinnkuimijugnia asimplificationfunctorforcoalgebras AT mauricekianpi simplificationfunctorforcoalgebras AT celestinnkuimijugnia simplificationfunctorforcoalgebras |