Multi-adjoint concept lattices via quantaloid-enriched categories

TL;DR

This paper demonstrates how multi-adjoint concept lattices and their variants can be derived from enriched category theory structures like Isbell, Kan, and dual Kan adjunctions within quantaloid-enriched categories.

Contribution

It introduces a categorical framework for multi-adjoint concept lattices using quantaloid-enriched categories and adjunctions, providing a unified theoretical foundation.

Findings

Multi-adjoint concept lattices are derivable from Isbell adjunctions.

Multi-adjoint property-oriented concept lattices are derived from Kan adjunctions.

Multi-adjoint object-oriented concept lattices come from dual Kan adjunctions.

Abstract

With quantaloids carefully constructed from multi-adjoint frames, it is shown that multi-adjoint concept lattices, multi-adjoint property-oriented concept lattices and multi-adjoint object-oriented concept lattices are derivable from Isbell adjunctions, Kan adjunctions and dual Kan adjunctions between quantaloid-enriched categories, respectively.