English

$\mathsf{Q}\text{-}\mathbf{Set}$ is not generally a topos

Category Theory 2025-06-04 v2

Abstract

For a commutative, unital and divisible quantale Q\mathsf{Q}, it is shown that the category of Q\mathsf{Q}-sets is a topos if, and only if, Q\mathsf{Q} is a frame.

Cite

@article{arxiv.2501.08559,
  title  = {$\mathsf{Q}\text{-}\mathbf{Set}$ is not generally a topos},
  author = {Xiao Hu and Lili Shen},
  journal= {arXiv preprint arXiv:2501.08559},
  year   = {2025}
}

Comments

15 pages, final version

R2 v1 2026-06-28T21:06:44.393Z