Abstract
Directed complete partially ordered sets (dcpos, for short) play an important role in domain theory. The aim of this paper is to characterise natural congruences of dcpos. We also show that the kernels of dcpo maps, that is, directed join-preserving maps between dcpos are not necessarily natural dcpo congruences. Then we characterise dcpo maps whose kernels are natural dcpo congruences. Finally, we prove the Decomposition and Isomorphism Theorems for dcpo maps.
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Presented by J. Adamek.
The first author would like to thank the Institute of Mathematics of the University of Warsaw for their kind hospitality during her stay on October 2013, also sincerely thanks SALAM representatives and coordinators in both home and host university for receiving scholarship under the Erasmus Mundus project.
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Mahmoudi, M., Moghbeli, H. & Pióro, K. Natural congruences and isomorphism theorems for directed complete partially ordered sets. Algebra Univers. 77, 79–99 (2017). https://doi.org/10.1007/s00012-017-0424-5
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DOI: https://doi.org/10.1007/s00012-017-0424-5