Glasnik Matematicki, Vol. 45, No.1 (2010), 173-217.

ON EXPANSIONS AND PRO-PRO-CATEGORIES

Nikica Uglešić and Vlasta Matijević

Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
e-mail: vlasta@pmfst.hr

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.

2000 Mathematics Subject Classification.   55P55, 18A32.

Key words and phrases.   Pro-category, pro-pro-category, expansion, pro-reflective subcategory, shape, polyhedron, compact Hausdorff space, completely regular space, Stone-Čech compactification, Hewitt realcompactification.

DOI: 10.3336/gm.45.1.13

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