On Bonds for Generalized One-Sided Concept Lattices

The generalized one-sided concept lattices represent a generalization of the classical FCA method convenient for a hierarchical analysis of object-attribute models with different types of attributes. The mentioned types of object-attribute models are formalized within the theory as formal contexts of a certain type. The aim of this paper is to investigate some intercontextual relationships represented by the notion of bond. A composition of bonds is defined in order to introduce the category of formal contexts with bonds as morphisms. It is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. As the main theoretical result it is shown that the introduced category of formal contexts with bonds is equivalent to the category of complete lattices with supremum preserving mappings as morphisms.

Automated summary

The paper investigates intercontextual relationships using the concept of bonds to explore the connections between different formal contexts. A composition of bonds is defined, and it is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. Furthermore, the category of formal contexts with bonds is proven to be equivalent to the category of complete lattices with supremum preserving mappings as morphisms.