Keywords: primary; 03B47; 03B55; 06D20; 06F05; secondary; 03G25; 03G27; Epimorphism; Brouwerian algebra; Heyting algebra; Esakia space; Residuated lattice; Sugihara monoid; Substructural logic; Intuitionistic logic; Relevance logic; R-mingle; Beth definability;