**Abstract.** In this paper we introduce the category Apro-ANR
called the approximate pro-category of ANR's, whose objects are all systems of ANR's and whose morphisms are
obtained as equivalence classes of system maps for some equivalence relation.
We show that any 2-sink
*X* →^{f} *Z* ←^{g} *Y**X* →^{f} *Z* ←^{g} *Y*

**2000 Mathematics Subject Classification.**
54C56, 54C55, 55U35.

**Key words and phrases.** Approximate pro-category, pull-back, approximate homotopy lifting property.

DOI: 10.3336/gm.43.2.15

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