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  "body": "\n## Summary\n\nA Stone-type duality for a variety or quasivariety of algebras is a dual equivalence of categories.\nIt matches the algebras with [[Stone spaces|ZV38HA5PAQ]] that carry additional structure.\nUnder it, homomorphisms of algebras correspond to continuous structure-preserving maps in the opposite direction.\nThe prototype is [[Stone duality|B9T33D5MJK]] between Boolean algebras and Stone spaces; [[Priestley duality|SA22SEC75K]] and Esakia duality for Heyting algebras are further examples.\nSuch dualities turn algebraic questions into topological ones, and the theory of [[natural dualities|W5VG6HS8KW]] gives a uniform method to build many of them.\n\n## Explanations\n\n### L1 human\n\nA Boolean algebra can be pictured as the clopen subsets of a compact, totally disconnected space, and this picture loses nothing.\nA Stone-type duality is a dictionary of this kind for another class of algebras.\nAlgebras become spaces, subalgebras become quotient spaces, quotients become subspaces, and products of finitely many algebras become disjoint unions of spaces.\nFor example, a finite distributive lattice corresponds to the finite ordered set of its join-irreducible elements.\n",
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