Simple omega-categories and chain complexes

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.

Keywords

simple omega-category, augmented directed complex, category of finite discs, globular cardinal, planar tree, level-tree, simple globular set, simple omega-graph, continuously graded ordered set, Batanin cell

2010 Mathematics Subject Classification

18D05

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Published 1 January 2007