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Meet-Semilattice Congruences on a Frame

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Abstract

The congruence lattice of a frame has long been an object of considerable interest, not least because it turns out to be a frame itself. Perhaps more surprisingly congruence lattices of, for instance, \(\sigma \)-frames, \(\kappa \)-frames and some partial frames also turn out to be frames. The situation for congruences of a meet-semilattice is notably different. In this paper we analyze the meet-semilattice congruence lattices of arbitrary frames and compare them with the corresponding lattices of frame congruences. In the course of this, we provide a structure theorem as well as many examples and counter-examples.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, 7701, Rondebosch, South Africa

    John Frith & Anneliese Schauerte

Authors
  1. John Frith
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  2. Anneliese Schauerte
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Correspondence to John Frith.

Additional information

Communicated by Bernhard Banaschewski.

Dedicated with appreciation to Bob Lowen on the occasion of his 70th birthday.

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Frith, J., Schauerte, A. Meet-Semilattice Congruences on a Frame. Appl Categor Struct 26, 997–1013 (2018). https://doi.org/10.1007/s10485-018-9521-7

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  • DOI: https://doi.org/10.1007/s10485-018-9521-7

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