Locally complete consistent F-augmented contexts: A category-theoretic representation of algebraic L-domains

In this paper, we demonstrate the capability of formal concept analysis in representing a special partially ordered structures named algebraic L-domains. In particular, we introduce the notion of locally complete consistent F-augmented contexts and prove that its associated category with F-approximable connections as morphisms is precisely equivalent to that of algebraic L-domains with Scott continuous functions as morphisms. This result provides a concrete representation of algebraic L-domains via formal concept analysis as an efficient approach.