Homomorphisms and principal congruences of bounded lattices. II. Sketching the proof for sublattices

TL;DR

This paper presents a new proof connecting the principal congruences of a bounded lattice with those of its bounded sublattice, enhancing understanding of their structural relationship.

Contribution

It provides a novel, streamlined proof of the relationship between principal congruences of bounded lattices and their sublattices.

Findings

Established a new proof for the relationship of principal congruences

Clarified the structural connection between lattices and sublattices

Simplified the understanding of principal congruences in bounded lattices

Abstract

A recent result of G. Cz\'edli relates the ordered set of principal congruences of a bounded lattice $L$ with the ordered set of principal congruences of a~bounded sublattice $K$ of $L$. In this note, I sketch a new proof.