Abstract
Motivated by the work of Hofmann [14] and Davey [7] on dualities for structures, we will construct natural dualities for the classes of quasi-ordered sets, equivalence-relationed sets, and reflexive (undirected) graphs. We describe the dual structures by giving finite sets of quasi-equations that axiomatise the dual categories. We also show that there is a natural connection between the duality we construct for finite quasi-ordered sets and Birkhoff’s representation theorem for finite ordered sets [2], and between the dualities constructed for quasi-ordered sets and equivalence-relationed sets.
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Johansen, S.M. Natural dualities for three classes of relational structures. Algebra Univers. 63, 149–170 (2010). https://doi.org/10.1007/s00012-010-0074-3
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DOI: https://doi.org/10.1007/s00012-010-0074-3