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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |