ordered-locale

What problem does it solve?

This Skill introduces ordered locales—frames enriched with a compatible preorder and the open cone condition—extending Stone duality to directed settings.

Core Features & Use Cases

• Frame-based Opens: Treats frame operations as subobject Heyting algebras.
• Preorder & Open Cones: Ensures upper and lower cones are open.
• Catlab Integration: Uses an ACSet schema to model ordered locales and their limits/colimits.
• Applications: Spacetime causality, domain theory, directed homotopy, and modal logic.

Quick Start

Run the demo commands (e.g., ordered-locale-demo) or verify the open cone condition with ordered-locale-verify; explore example locales like the Sierpinski or diamond locale.