ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS

Concrete categories of functorial coalgebras are derived from given concrete categories under a certain commutativity condition satisfied by the underlying forgetful functor and endofunctors of its domain and codomain. When the base category is topological, so is that of functorial coalgebras when in addition to the commutativity condition the endofunctor of its domain preserves initial sources. We investigate the connection between fibres of objects in the topological category of coalgebras and those of the topological base category as well as some generalizations of the coalgebraic topological functor.