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• W2996044461 startingPage "419" @default.
• W2996044461 abstract "We introduce constructible directed complexes, a combinatorial presentation of higher categories inspired by constructible complexes in poset topology. Constructible directed complexes with a greatest element, called atoms, encompass common classes of higher-categorical cell shapes, including globes, cubes, oriented simplices, and a large sub-class of opetopes, and are closed under lax Gray products and joins. We define constructible polygraphs to be presheaves on a category of atoms and inclusions, and extend the monoidal structures. We show that constructible directed complexes are a well-behaved subclass of Steiner’s directed complexes, which we use to define a realisation functor from constructible polygraphs to $$omega $$-categories. We prove that the realisation of a constructible polygraph is a polygraph in restricted cases, and in all cases conditionally to a conjecture. Finally, we define the geometric realisation of a constructible polygraph, and prove that it is a CW complex with one cell for each of its elements." @default.
• W2996044461 created "2019-12-26" @default.
• W2996044461 creator A5073235643 @default.
• W2996044461 date "2019-11-30" @default.
• W2996044461 modified "2023-09-25" @default.
• W2996044461 title "A Combinatorial-Topological Shape Category for Polygraphs" @default.
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• W2996044461 doi "https://doi.org/10.1007/s10485-019-09586-6" @default.
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