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arXiv · 2507.20768

A Completeness Theorem for Topological Doctrines

Silvio Ghilardi·Jérémie Marquès
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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.

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Silvio Ghilardi, Jérémie Marquès. 2025-07-28. A Completeness Theorem for Topological Doctrines. https://arxiv.org/abs/2507.20768

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