---
_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: 2023-11-20T09:24:48Z
day: '01'
department:
- _id: HeEd
doi: 10.2989/16073606.2023.2247731
intvolume: '        46'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2023'
...
---
_id: '12764'
abstract:
- lang: eng
  text: We study a new discretization of the Gaussian curvature for polyhedral surfaces.
    This discrete Gaussian curvature is defined on each conical singularity of a polyhedral
    surface as the quotient of the angle defect and the area of the Voronoi cell corresponding
    to the singularity. We divide polyhedral surfaces into discrete conformal classes
    using a generalization of discrete conformal equivalence pioneered by Feng Luo.
    We subsequently show that, in every discrete conformal class, there exists a polyhedral
    surface with constant discrete Gaussian curvature. We also provide explicit examples
    to demonstrate that this surface is in general not unique.
acknowledgement: Open access funding provided by the Austrian Science Fund (FWF).
  This research was supported by the FWF grant, Project number I4245-N35, and by the
  Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID
  195170736 - TRR109.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Hana
  full_name: Kourimska, Hana
  id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
  last_name: Kourimska
  orcid: 0000-0001-7841-0091
citation:
  ama: Kourimska H. Discrete yamabe problem for polyhedral surfaces. <i>Discrete and
    Computational Geometry</i>. 2023;70:123-153. doi:<a href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>
  apa: Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. <i>Discrete
    and Computational Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>
  chicago: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete
    and Computational Geometry</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>.
  ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” <i>Discrete
    and Computational Geometry</i>, vol. 70. Springer Nature, pp. 123–153, 2023.
  ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete
    and Computational Geometry. 70, 123–153.
  mla: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete
    and Computational Geometry</i>, vol. 70, Springer Nature, 2023, pp. 123–53, doi:<a
    href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>.
  short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.
date_created: 2023-03-26T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-10-04T11:46:48Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00484-2
external_id:
  isi:
  - '000948148000001'
file:
- access_level: open_access
  checksum: cdbf90ba4a7ddcb190d37b9e9d4cb9d3
  content_type: application/pdf
  creator: dernst
  date_created: 2023-10-04T11:46:24Z
  date_updated: 2023-10-04T11:46:24Z
  file_id: '14396'
  file_name: 2023_DiscreteGeometry_Kourimska.pdf
  file_size: 1026683
  relation: main_file
  success: 1
file_date_updated: 2023-10-04T11:46:24Z
has_accepted_license: '1'
intvolume: '        70'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 123-153
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Discrete and Computational Geometry
publication_identifier:
  eissn:
  - 1432-0444
  issn:
  - 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete yamabe problem for polyhedral surfaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2023'
...