Year: 2025
Type: article
Abstract: 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, locally small, and small-complete frames with small bases. This requires predicative reformulations of several fundamental concepts of locale theory in predicative HoTT/UF , which we investigate systematically.
Authors: Igor Arrieta, Martín H. Escardó, Ayberk Tosun
Institution: University of Birmingham
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Funder: Eusko Jaurlaritza
Awards: G1125825615, G2748340936
OpenAlex ID: W4413022543