Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

Simple omega-categories and chain complexes

Pages: 451 – 465

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a18


Richard Steiner (Department of Mathematics, University of Glasgow, Scotland, United Kingdom)


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.


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


Published 1 January 2007