The algebra of directed complexes |
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Authors: | Richard Steiner |
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Affiliation: | (1) Department of Mathematics, University of Glasgow, University Gardens, G12 8QW Glasgow, Scotland |
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Abstract: | The theory of directed complexes is a higher-dimensional generalisation of the theory of directed graphs. In a directed graph, the simple directed paths form a subset of the free category which they generate; if the graph has no directed cycles, then the simple directed paths constitute the entire category. Generalising this, in a directed complex there is a class of split subsets which is contained in and generates a free -category; when a simple loop-freeness condition is satisfied, the split sets constitute the entire -category. The class of directed complexes is closed under the natural product and join constructions. The free -categories generated by directed complexes include the important examples associated to cubes and simplexes. |
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Keywords: | 18D05 |
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