Corpus ID: 202676692

A new Galois structure in the category of internal preorders

@article{Facchini2019ANG,
  title={A new Galois structure in the category of internal preorders},
  author={A. Facchini and C. Finocchiaro and M. Gran},
  journal={arXiv: Category Theory},
  year={2019}
}
  • A. Facchini, C. Finocchiaro, M. Gran
  • Published 2019
  • Mathematics
  • arXiv: Category Theory
  • Let $\mathsf{PreOrd}(\mathbb C)$ be the category of internal preorders in an exact category $\mathbb C$. We show that the pair $(\mathsf{Eq}(\mathbb C), \mathsf{ParOrd}(\mathbb C))$ is a pretorsion theory in $\mathsf{PreOrd}(\mathbb C)$, where $\mathsf{Eq}(\mathbb C)$ and $\mathsf{ParOrd}(\mathbb C)$) are the full subcategories of internal equivalence relations and of internal partial orders in $\mathbb C$, respectively. We observe that $\mathsf{ParOrd}(\mathbb C)$ is a reflective subcategory… CONTINUE READING
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