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PreprintCC BY-NC-ND 4.0arXiv

Cartesian closedness of the category of real-valued sets, II

  • Lili Shen
  • Jian Zhang
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Abstract

Let [0,1]* be the unit interval [0,1] equipped with a left-continuous t-norm *. We prove that [0,1]*−Set is cartesian closed if and only if * is the minimum t-norm. This extends the classification for continuous t-norms established in the first part of this work to the whole left-continuous setting.

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Cite

BibTeXRIS
BibTeX
@misc{shen2026cartesian,
  title = {{Cartesian closedness of the category of real-valued sets, II}},
  author = {Lili Shen and Jian Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05929},
  eprint = {2609.05929},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05929},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Cartesian closedness of the category of real-valued sets, II
AU  - Lili Shen
AU  - Jian Zhang
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05929
UR  - https://arxiv.org/abs/2609.05929
AB  - Let [0,1]_* be the unit interval [0,1] equipped with a left-continuous t-norm *. We prove that [0,1]_*−Set is cartesian closed if and only if * is the minimum t-norm. This extends the classification for continuous t-norms established in the first part of this work to the whole left-continuous setting.
ER  -