English

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.

Keywords

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

R2 v1 2026-07-01T04:21:59.859Z