The Minor Order of Homomorphisms via Natural Dualities

TL;DR

This paper explores the structure of algebra homomorphisms in certain algebraic varieties using natural dualities, providing a detailed characterization of their minor relations and addressing homomorphism reconstruction challenges.

Contribution

It introduces a new characterization of minor homomorphism posets in finitely generated quasivarieties with natural dualities, linking them to dual partition lattices.

Findings

Minor relation for homomorphisms characterized by dual partition lattices

Reconstruction problems for homomorphisms analyzed

Structural insights into homomorphism posets in quasivarieties

Abstract

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize the minor homomorphism posets of finite algebras in terms of disjoint unions of dual partition lattices and investigate reconstruction problems for homomorphisms.