Congruence frames of frames and $\kappa$-frames

TL;DR

This paper investigates the structure of congruence lattices in frames and $$-frames, exploring their categorical properties and the role of congruence biframes in zero-dimensional contexts.

Contribution

It provides a detailed description of congruence lattices for frames and $$-frames and examines the categorical relationships involving congruence biframes.

Findings

Characterization of congruence lattices for frames and $$-frames

Analysis of congruence biframes in zero-dimensional categories

Discussion of reflections and coreflections related to congruence frames

Abstract

We describe the congruence lattices of frames and $\kappa$-frames. We look at the role that congruence biframes play in the category of strictly zero-dimensional biframes and discuss some reflections and coreflections of congruence frames.