The fundamental duality of partially ordered sets
The authors embed posets, lattices, and frames in the category \(\underset \tilde{} P\) of posets with an arbitrary family of joins and an arbitrary family of meets distinguished. (Thus, posketches.) Universal maps from objects of \(\underset \tilde{} P\) to posets of all subsets with unions and intersections were constructed by the second author in J. Reine Angew. Math. 209, 167-200, and 210, 1-23 (1962; Zbl 0148.012). This is now amplified to a Galois connection (or imperfect ``duality'') extending several familiar connections and dualities. The objects of the second category generalize topological spaces and closure spaces.
scientific article; zbMATH DE number 4065054