A Completeness Theorem for Topological Doctrines
Category Theory
2025-07-29 v1 Logic
Abstract
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product independence' and a `loop contraction' principle.
Cite
@article{arxiv.2507.20768,
title = {A Completeness Theorem for Topological Doctrines},
author = {Silvio Ghilardi and Jérémie Marquès},
journal= {arXiv preprint arXiv:2507.20768},
year = {2025}
}
Comments
29 pages