Monomorphisms of Coalgebras
نویسنده
چکیده
In any concrete category C the natural problem of whether epimorphisms are surjective maps arise, as well as the dual problem of whether the monomorphisms are injective maps. This type of problems have already been studied before in several well known categories: for example in [6] it is shown that the property of epimorphisms of being surjective holds in the categories of von Neumann algebras, C-algebras, groups, finite groups, Lie algebras, compact groups, while it fails to be true in the categories of finite dimensional Lie algebras, semisimple finite dimensional Lie algebras and locally compact groups. The more recent paper [3] deals with the same problems in the context of Hopf algebras: several examples of non-injective monomorphisms and non-surjective epimorphisms are given. It turns out that the above problem is also intimately related to Kaplansky’s first conjecture in the way that every non-surjective epimorphism of Hopf algebras provides an counterexample to Kaplansky’s problem.
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