Orientals

Details Orientals Orientals

2006-01-16

arxiv.org/abs/math/0601383v2

Contemporary Mathematics 431 (2007) 427-439

Mathematics

Category Theory

13 pages; version 2 has misprints corrected

Scientific paper

The orientals or oriented simplexes are a family of strict omega-categories constructed by Ross Street. We show that the category of orientals is isomorphic to a subcategory of the category of chain complexes. This leads to a very simple combinatorial description of the morphisms between orientals. We also show that the category of orientals is the closure of the category of simplexes under certain filler operations which represent complicial operations.

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