A simplification functor for coalgebras

Maurice Kianpi and Celestin Nkuimi Jugnia

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

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 ofsimple 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 theinclusion of the subcategory of simple coalgebras into the category S e t F 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. Inparticular, if a product of simple coalgebras exists, this is simple too.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:056786

DOI: 10.1155/IJMMS/2006/56786

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