Positive varieties of regular lattice languages are in bijection with pseudo-varieties of finite ordered monoids, generalizing Pin's positive variety theorem.
Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited.Forum Mathematicum, 26(6):1737–1761, 2014
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Positive Varieties of Lattice Languages
Positive varieties of regular lattice languages are in bijection with pseudo-varieties of finite ordered monoids, generalizing Pin's positive variety theorem.