Retractable and coretractable modules in Wisbauer category (Q2170471)

A module \(M\) is retractable if whenever \(N\) is a non-zero submodule, Hom\((M,\, N)\ne 0\) and coretractable if whenever \(K\) is a non-zero epimorphic image, Hom\((K,M)\ne 0\). The authors identify several classes of modules which are retractable if and only if they are coretractable; for example, they show that in the case of a coalgebra over a field, every right comodule is retractable if and only if every right comodule is coretractable.