Strictly zero-dimensional biframes and a characterisation of congruence frames

Abstract

Strictly zero-dimensional biframes were introduced by Banaschewski and Br\"{u}mmer as a class of strongly zero-dimensional biframes including the congruence biframes. We consider the category of strictly zero-dimensional biframes and show it is both complete and cocomplete. We characterise the extremal monomorphisms in this category and explore the special position that congruence biframes hold in it. Finally, we provide an internal characterisation of congruence biframes, and hence, of congruence frames.