A Completeness Theorem for Topological Doctrines

2025/07/28 by Ghilardi, Silvio, Marquès, Jérémie
#03B45 #03C80 #03G30 #18F60 #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2507.20768

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.

Citations

• First-Order Modal Logic via Logical Categories
• Elementary quotient completion

Related

• The Geometric Completion of a Doctrine
• Knowledge Theoretic Properties of Topological Spaces
• Lawvere completion and separation via closure
• Topological Completeness for Higher-Order Logic
• The doctrinal Gödel's completeness theorem and the type space functor