Geodesic
The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 21-36.

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Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.
Keywords: hypersubstitutions, hyperidentities, M-hyperidentities, monoids of hypersubstitutions, varieties, solid varieties, M-solid varieties of bands, Galois correspondence 
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Denecke, Klaus; Hyndman, Jennifer; Wismath, Shelly. The Galois correspondence between subvariety lattices and monoids of hpersubstitutions. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 21-36. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a1/

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