---
_id: '14557'
abstract:
- lang: eng
  text: 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.
acknowledgement: "The first and second named authors are members of GNSAGA – INdAM.\r\nThe
  third named author was supported by the FWF Grant, Project number I4245–N35"
article_processing_charge: No
article_type: original
author:
- first_name: D.
  full_name: Dikranjan, D.
  last_name: Dikranjan
- first_name: A.
  full_name: Giordano Bruno, A.
  last_name: Giordano Bruno
- first_name: Nicolò
  full_name: Zava, Nicolò
  id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
  last_name: Zava
  orcid: 0000-0001-8686-1888
citation:
  ama: 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>
  apa: 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>
  chicago: 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>.
  ieee: 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.
  ista: Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators
    of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.
  mla: 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>.
  short: D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023)
    191–221.
date_created: 2023-11-19T23:00:55Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T13:23:12Z
day: '01'
department:
- _id: HeEd
doi: 10.2989/16073606.2023.2247731
external_id:
  isi:
  - '001098712000006'
intvolume: '        46'
isi: 1
issue: S1
language:
- iso: eng
month: '11'
oa_version: None
page: 191-221
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Quaestiones Mathematicae
publication_identifier:
  eissn:
  - 1727-933X
  issn:
  - 1607-3606
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Epimorphisms and closure operators of categories of semilattices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 46
year: '2023'
...