Armstrong systems and Galois connections
Michiro Kondo, Sho Soneda, Bunpei Yoshii · 2011
In the paper [1], it is proved that any Galois connection (f, g) on a complete lattice made an Armstrong system F(f, g). We prove in this short note that the converse holds, that is, for a given Armstrong system R, we can make a Galois connection (φR, ψR) and the original Armstrong system R is identical with the induced Armstrong system F(φR, ψR)by the Galois connection (φR, ψR). This means that Armstrong systems and Galois connections show us two faces of one thing.