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Sep 4 at 20:46 history edited Keith Kearnes CC BY-SA 4.0
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Sep 3 at 20:31 history bounty ended Gejza Jenča
Sep 2 at 17:56 comment added Jochen Wengenroth Thanks a lot for adding all the details.
Sep 2 at 15:11 history edited Keith Kearnes CC BY-SA 4.0
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Sep 2 at 15:01 history edited Keith Kearnes CC BY-SA 4.0
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Sep 2 at 12:51 comment added Jochen Wengenroth There are no references given on math.chapman.edu/~jipsen/structures and after superficially reading the article of Jónsson it seems to me that his argument is similar to the one in the deleted answer of Gejza Jenca: Condider an equalizer in the category POS of posets and take the Dedekind-MacNeill completion to get a lattice. The question is whether the morphisms constructed in POS making $f$ an equalizer are lattice morphisms. This seems to be similar to the problem in the deleted answer of Pietro Majer.
Sep 1 at 18:11 vote accept Dominic van der Zypen
Sep 1 at 16:00 history answered Keith Kearnes CC BY-SA 4.0