We propose a convenient category for directed homotopy consisting of "directed'' topological spaces generated by "directed'' cubes. Its main advantage is that, like the category of topological spaces generated by simplices suggested by J. H. Smith, it is locally presentable.
Keywords: locally presentable category, simplex-generated spaces, directed homotopy, dicovering
2000 MSC: Primary 18C35; Secondary 55P99, 68Q85
Theory and Applications of Categories,
Vol. 21, 2008,
No. 1, pp 7-20.
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