Morphisms in Context


Abstract. Morphisms constitute a general tool for modelling complex relationships between mathematical objects on a large scale. In Formal Concept Analysis (FCA), morphisms can therefore be used for the study of structural properties of the knowledge represented in formal contexts, with applications to data transformation and merging. In this paper we present a comprehensive treatment of some of the most important morphisms in FCA and their relationships, which includes the study of dual bonds, scale measures, infomorphisms and their respective relations to Galois connections. We summarize our results in a concept lattice that displays all relationships between the considered morphisms. The purpose of this foundational work is to provide a basis for future applications of FCA in ontology research and similar areas, where morphisms provide a way to formalize the interplay between distributed knowledge bases.

Published at ICCS2005 (Conference paper)

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Formal Concept Analysis, Algebra and order