A cellular nerve for higher categories

Abstract

We realise Joyal's cell category Θ as a dense subcategory of the category of ω-categories. The associated cellular nerve of an ω-category extends the well-known simplicial nerve of a small category. Cellular sets (like simplicial sets) carry a closed model structure in Quillen's sense with weak equivalences induced by a geometric realisation functor. More generally, there exists a dense subcategory ΘA of the category of A-algebras for each ω-operad A in Batanin's sense. Whenever A is contractible, the resulting homotopy category of A-algebras (i.e. weak ω-categories) is equivalent to the homotopy category of compactly generated spaces. © 2002 Elsevier Science (USA).