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.
http://www.tac.mta.ca/tac/volumes/21/5/21-05.dvi
http://www.tac.mta.ca/tac/volumes/21/5/21-05.ps
http://www.tac.mta.ca/tac/volumes/21/5/21-05.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/21/5/21-05.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/21/5/21-05.ps