On the definition of suitable orderings to generate adjunctions over an unstructured codomain. (English) Zbl 1355.06011
Summary: Given a mapping \(f : A \to B\) from a (pre-)ordered set \( A\) into an unstructured set \( B\), we study the problem of defining a suitable (pre-)ordering relation on \( B\) such that there exists a mapping \(g : B \to A\) such that the pair of mappings \((f, g)\) forms an adjunction between (pre-)ordered sets. The necessary and sufficient conditions obtained are then expressed in terms of closure operators and closure systems.
MSC:
| 06A15 | Galois correspondences, closure operators (in relation to ordered sets) |
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