article published yes D. Dikranjan author A. Giordano Bruno author Nicolò Zava author c8b3499c-7a77-11eb-b046-aa368cbbf2ad0000-0001-8686-1888 HeEd department Algebraic Footprints of Geometric Features in Homology project 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 & Francis2023 eng 1607-3606 1727-933X 00109871200000610.2989/16073606.2023.2247731 46S1191-221 Dikranjan, D., Giordano Bruno, A., &#38; Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>. Taylor &#38; Francis. <a href="https://doi.org/10.2989/16073606.2023.2247731">https://doi.org/10.2989/16073606.2023.2247731</a> Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>. Taylor &#38; Francis, 2023. <a href="https://doi.org/10.2989/16073606.2023.2247731">https://doi.org/10.2989/16073606.2023.2247731</a>. Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1, Taylor &#38; Francis, 2023, pp. 191–221, doi:<a href="https://doi.org/10.2989/16073606.2023.2247731">10.2989/16073606.2023.2247731</a>. D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1. Taylor &#38; Francis, pp. 191–221, 2023. D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221. Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221. 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> 145572023-11-19T23:00:55Z2025-09-09T13:23:12Z