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Dikranjan, D.; Giordano Bruno, A.; Zava, N.
Quaestiones mathematicae, 11/2023, Letnik: 46, Številka: S1Journal Article
Motivated by a problem posed in 10, we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLatt O of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLatt O are surjective. We complement the paper with two different proofs of this result using either generators or Isbell's zigzag theorem.
