The Patch Topology in Univalent Foundations
<|reference_start|>The Patch Topology in Univalent Foundations: Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be easily translated to univalent type theory using resizing axioms. In this work, we show how to achieve such a translation without resizing axioms, by working with large and locally small frames with small bases. This requires predicative reformulations of several fundamental concepts of locale theory in predicative HoTT/UF, which we investigate systematically.<|reference_end|>
@article{arrieta2024the,
    title={The Patch Topology in Univalent Foundations},
    author={Igor Arrieta, Mart'in H"otzel Escard'o, Ayberk Tosun},
    journal={arXiv preprint arXiv:2402.03134},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03134},
    primaryClass={cs.LO}
}