On expansions and pro-pro-categories (CROSBI ID 150690)
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Podaci o odgovornosti
Uglešić, Nikica ; Matijević, Vlasta
engleski
On expansions and pro-pro-categories
If (C, D) is a category pair such that D⊆ C is a pro-reflective subcategory, then so is D⊆ pro-C and, inductively, D⊆ proⁿ 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.
pro-category; pro-pro-category; expansion; pro-reflective subcategory; shape; Stone-Čech compactification; Hewitt realcompactification
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