A representation of FS-domains by formal concept analysis (Q2064935)

The category \texttt{Dom} of continuous domains with Scott continuous functions is not cartesian closed while from [\textit{A. Jung}, Cartesian closed categories of domains. Amsterdam: Centrum voor Wiskunde en Informatica (1989; Zbl 0719.06004); ``The classification of continuous domains'', in: Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science. Los Alamitos,CA: IEEE Computer Society. 35--40 (1990)] it is known that the full subcategory \texttt{FSD} of \textit{FS-domains} (a pointed dcpo with a directed set of continuous endomorphisms, each finitely separated from the identity morphism and having the identity morphism as its supremum [\textit{S. Abramsky} and \textit{A. Jung}, Domain theory, corrected and expanded version. \url{https://www.cs.bham.ac.uk/~axj/pub/papers/handy1.pdf}]) is maximal cartesian closed. The present paper proposes a notion of \textit{FS-contexts} (based on the notion of \textit{contractive operators} in [\textit{L. Wang} et al., Fundam. Inform. 179, No. 3, 295--319 (2021; Zbl 07426112)]) and shows: each FS-domain, upto isomorphism, is the set of FS-formal concepts of a FS-context.