Geodesic
Linear programming duality and morphisms
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 577-592.

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In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids.
Classification : 05B35, 05C99, 18B99, 52C40, 90C05, 90C27, 90C46
Keywords: oriented matroids; strong maps; homomorphisms; duality 
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Hochstättler, Winfried; Nešetřil, Jaroslav. Linear programming duality and morphisms. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 577-592. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a16/