  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.
