  Formal Concept Analysis has proven to be an effective method of restructuring
complete lattices and various algebraic domains. In this paper, the notions of
attribute continuous formal context and continuous formal concept are
introduced by considering a selection F of fnite subsets of attributes. Our
decision of a selection F relies on a kind of generalized interior operators.
It is shown that the set of continuous formal concepts forms a continuous
domain, and every continuous domain can be obtained in this way. Moreover, an
notion of F-morphism is also identified to produce a category equivalent to
that of continuous domains with Scott-continuous functions. This paper also
consider the representations of various subclasses of continuous domains such
as algebraic domains, bounded complete domains and stably continuous
semilattices. These results explore the fundamental idea of domain theory in
Formal Concept Analysis from a categorical viewpoint.
