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Linear programming duality and morphisms. (English) Zbl 1065.05027
The paper concerns the problems of “good characterization”. A class $$K$$ of objects together with a certain class of homomorphisms between them is considered. The symbol $$A\rightarrow B$$ means that there is a homomorphism from $$A$$ to $$B$$. Further $$\rightarrow (A): = \{B \in K\mid B\rightarrow A\}$$, $$(A) \rightarrow : = \{B\in K\mid A\rightarrow B\}$$. The complementary classes are denoted by $$\not \rightarrow (A)$$ and $$(A) \not \rightarrow$$. A homomorphism duality theorem for $$K$$ is then an equality of the type $$(B) \rightarrow = \not \rightarrow (A)$$. These homomorphism dualities are investigated for graphs (both directed and undirected), and for oriented matroids (they are defined in the paper). On oriented matroids various types of mappings are studied (strong maps, affine strong maps).

##### MSC:
 05B35 Combinatorial aspects of matroids and geometric lattices 18B99 Special categories 90C05 Linear programming 52C40 Oriented matroids in discrete geometry
##### Keywords:
oriented matroid; strong map; homomorphism; duality
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