G. Czédli’s tolerance factor lattice construction and weak ordered relations

Abstract G. Czédli proved that the blocks of any compatible tolerance T a lattice L can be ordered in such way they form / called factor modulo . Here we show Dedekind–MacNeille completion is isomorphic to concept context ( , R ), where stands for reflexive weak relation $$ \mathord {\le } \circ T$$ ≤ ∘ T Weak relations constitute generalization introduced by S. Valentini. Reflexive characterized as $$R\subseteq L^{2}$$ R ⊆ L 2 satisfying $$R=\ R\circ =