Original scientific paper

https://doi.org/10.3336/gm.45.1.13

On expansions and pro-pro-categories

Nikica Uglešić ; University of Zadar, Pavlinovićeva bb, 23000 Zadar, Croatia
Vlasta Matijević ; Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia

Abstract

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 pronC 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.

Keywords

Pro-category; pro-pro-category; expansion; pro-reflective subcategory; shape; polyhedron; compact Hausdorff space; completely regular space; Stone-Čech compactification; Hewitt realcompactification

Hrčak ID:

52375

URI

https://hrcak.srce.hr/52375

Publication date:

17.5.2010.

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