Simple omega-categories and chain complexes

Details Simple omega-categories and chain complexes Simple omega-categories and chain complexes

2006-08-28

arxiv.org/abs/math/0608680v2

Homotopy, Homology and Applications 9(1), 2007, 451-465

Mathematics

Category Theory

14 pages; v2 has minor corrections and a little additional material

Scientific paper

The category of strict omega-categories has an important full subcategory whose objects are the simple omega-categories freely generated by planar trees or by globular cardinals. We give a simple description of this subcategory in terms of chain complexes, and we give a similar description of the opposite category, the category of finite discs, in terms of cochain complexes. Berger has shown that the category of simple omega-categories has a filtration by iterated wreath products of the simplex category. We generalise his result by considering wreath products of categories of chain complexes over the simplex category.

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