On expansions and pro-pro-categories
Nikica Uglešić, Vlasta Matijević · Glasnik Matematicki · 2010
If (C, D) is a category pair such that D ⊆ C is a proreflective subcategory, then so is D ⊆ pro-C and, inductively, D ⊆ pro n C as well.The key fact is that the terms and morphisms of D-expansions of all the terms of a C-system can be naturally organized in a D-expansion of the system.Therefore, in dealing with expansions, there is no need to involve the pro-pro-category technique.In particular, the shape of a C-system, as well as of a C-object, reduces to the isomorphism class of a D-system.On the other hand, a pro-pro-category could be useful for some other purposes because it admits functorial expansions which are inverse limits.Some applications of the theoretical part are considered, especially, concerning the Stone-Čech compactification and Hewitt realcompactification.