Concept lattices of Q-relations via diagonal and back-diagonal categories

@misc{lai2026concept,
  title = {{Concept lattices of $Q$-relations via diagonal and back-diagonal categories}},
  author = {Hongliang Lai and Bo Pang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13809},
  eprint = {2609.13809},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13809},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Concept lattices of Q-relations via diagonal and back-diagonal categories
AU  - Hongliang Lai
AU  - Bo Pang
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13809
UR  - https://arxiv.org/abs/2609.13809
AB  - Let Q be a commutative unital quantale and QRel the ordered category of sets and Q-relations. We develop a categorical foundation for formal and property-oriented concept lattices of Q-relations via the diagonal category DQRel and back-diagonal category BQRel. Our main results are: (1) the formal concept lattice construction is induced by a representable functor on BQRel; (2) the property-oriented concept lattice construction corresponds to a representable functor on DQRel; and (3) for regular Q-relations, the property-oriented concept lattice of their pointwise tensor product is naturally isomorphic to the tensor product of the respective property-oriented concept lattices.
ER  -