Completions in biaffine sets

Elisabetta Felaco and Eraldo Giuli

The theory of completion of $T_0$ objects in categories of affine objects over a given complete category developed by the second author is extended to the case of $T_0$ objects in categories of 2affine objects. In the paper the case of the category $Set$ and target object the two-point set is studied in detail and an internal characterization of 2affine sets is provided.

Keywords: 2affine set, Zariski closure, separated object, complete object, injective object, bitopological space}

2000 MSC: 18A20, 18B30, 18B99, 18A32, 08B30, 54A05, 54B30

Theory and Applications of Categories, Vol. 21, 2008, No. 5, pp 76-90.

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