I'll present a common characterization of the duality relations associated with matroids, oriented matroids, and related objects.
This is from a paper by Robert G. Bland and Brenda L. Dietrich, "A unified interpretation of several combinatorial dualities" (Discrete Optimization 5 (2008), no. 2, 337–349).
This is the second half of Ms. Su's admission-to-candidacy examination. The examining committee consists of Laura Anderson (chair), Michael Dobbins, and Thomas Zaslavsky.