Scientific publications
Célestin Nkuimi Jugnia
International Journal of Mathematics and Mathematical Sciences
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 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.
