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
*pro*-C*pro*^{n}C

**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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