Abstract
A new method is introduced for simplifying finite directed cubical complexes. This construction is effective in the sense that it can be computed relatively efficiently, and it induces a fully faithful inclusion on path categories. The resulting parallelized family of algorithms enables calculations of morphism sets of path categories of such complexes in many cases of practical interest, and working code is provided as a proof of concept.
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Acknowledgments
I would like to thank Professor Rick Jardine for introducing me to these applications of homotopy theory to computer science. The anonymous referee is also thanked for providing helpful comments which improved the exposition.
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Misamore, M.D. Computing path categories of finite directed cubical complexes. AAECC 26, 151–164 (2015). https://doi.org/10.1007/s00200-014-0243-2
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DOI: https://doi.org/10.1007/s00200-014-0243-2