Epimorphisms and closure operators of categories of semilattices Dikranjan, D. Giordano Bruno, A. Zava, Nicolò ; https://orcid.org/0000-0001-8686-1888 Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO 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 SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem. Taylor & Francis 2023 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/14557 Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>. 2023;46(S1):191-221. doi:<a href="https://doi.org/10.2989/16073606.2023.2247731">10.2989/16073606.2023.2247731</a> eng info:eu-repo/semantics/altIdentifier/doi/10.2989/16073606.2023.2247731 info:eu-repo/semantics/altIdentifier/issn/1607-3606 info:eu-repo/semantics/altIdentifier/e-issn/1727-933X info:eu-repo/semantics/altIdentifier/wos/001098712000006 info:eu-repo/semantics/closedAccess