A convenient category for directed homotopy

We propose a convenient category for directed homotopy consisting of preordered topological spaces generated by cubes. Its main advantage is that, like the category of topological spaces generated by simplices suggested by J. H. Smith, it is locally presentable.

💡 Research Summary

The paper introduces a new categorical framework for directed homotopy that is both conceptually simple and technically robust. The authors focus on preordered topological spaces—pairs (X, ≤) where X is a topological space and ≤ is a reflexive, transitive relation compatible with the topology in the sense that directed paths (continuous maps γ: