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PreprintCC BY 4.0arXiv

A note on coextensivity of bounded hoops

  • Michael Hoefnagel
  • Giuseppe Metere
  • Danielle Kleyn
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Abstract

The main aim of this note is to provide a characterisation of coextensive morphisms in the category of bounded hoops. This characterisation is then used to show that several categories of bounded hoops are coextensive as categories. Among these are the variety of bounded Wajsberg hoops, or more generally the variety of bounded ∨-hoops. Our characterisation also yields the coextensivity of the category Heyt of Heyting algebras and recovers the known coextensivity of the category MV of MV-algebras.

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Cite

BibTeXRIS
BibTeX
@misc{hoefnagel2026note,
  title = {{A note on coextensivity of bounded hoops}},
  author = {Michael Hoefnagel and Giuseppe Metere and Danielle Kleyn},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.30476},
  eprint = {2608.30476},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30476},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A note on coextensivity of bounded hoops
AU  - Michael Hoefnagel
AU  - Giuseppe Metere
AU  - Danielle Kleyn
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.30476
UR  - https://arxiv.org/abs/2608.30476
AB  - The main aim of this note is to provide a characterisation of coextensive morphisms in the category of bounded hoops. This characterisation is then used to show that several categories of bounded hoops are coextensive as categories. Among these are the variety of bounded Wajsberg hoops, or more generally the variety of bounded ∨-hoops. Our characterisation also yields the coextensivity of the category Heyt of Heyting algebras and recovers the known coextensivity of the category MV of MV-algebras.
ER  -