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PreprintCC BY 4.0arXiv

Products of Boolean Clones up to Minion Homomorphisms

  • Radek Olšák
Open at sourcePDFDOICite

Abstract

We study the minion homomorphism poset of multisorted Boolean clones. Our main result completely determines the subposet induced by products of Boolean clones: every inequality between prod- ucts is induced by inequalities between their Boolean factors. Furthermore, we determine the minion cores of all products of Boolean clones, thereby identifying canonical representatives of their minion homomorphic equivalence classes.

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Cite

BibTeXRIS
BibTeX
@misc{olsak2026products,
  title = {{Products of Boolean Clones up to Minion Homomorphisms}},
  author = {Radek Olšák},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12484},
  eprint = {2610.12484},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12484},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Products of Boolean Clones up to Minion Homomorphisms
AU  - Radek Olšák
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.12484
UR  - https://arxiv.org/abs/2610.12484
AB  - We study the minion homomorphism poset of multisorted Boolean clones. Our main result completely determines the subposet induced by products of Boolean clones: every inequality between prod- ucts is induced by inequalities between their Boolean factors. Furthermore, we determine the minion cores of all products of Boolean clones, thereby identifying canonical representatives of their minion homomorphic equivalence classes.
ER  -