Abstract
Strictly zero-dimensional biframes were introduced by Banaschewski and Brümmer 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 epimorphisms 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.
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Communicated by B. Banaschewski.
I acknowledge financial assistance from the National Research Foundation of South Africa (Grant No. 89726).
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Manuell, G. Strictly Zero-Dimensional Biframes and a Characterisation of Congruence Frames. Appl Categor Struct 26, 645–655 (2018). https://doi.org/10.1007/s10485-017-9507-x
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DOI: https://doi.org/10.1007/s10485-017-9507-x