  Representation theorems are established for fixed points of adjoint functors
between categories enriched in a small quantaloid. In a very general setting
these results set up a common framework for representation theorems of concept
lattices in formal concept analysis (FCA) and rough set theory (RST), which not
only extend the realm of formal contexts to multi-typed and multi-valued ones,
but also provide a general approach to construct various kinds of
representation theorems. Besides incorporating several well-known
representation theorems in FCA and RST as well as formulating new ones, it is
shown that concept lattices in RST can always be represented as those in FCA
through relative pseudo-complements of the given contexts, especially if the
contexts are valued in a non-Girard quantaloid.
