Journal
ADVANCES IN MATHEMATICS
Volume 169, Issue 1, Pages 118-175Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/aima.2001.2056
Keywords
higher categories; globular operads; combinatorial homotopy
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We realise Joyal's cell category Theta as a dense subcategory of the category of omega-cocategories. The associated cellular nerve of an omega-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 Theta(A) of the category of A-algebras for each omega-operad A in Batanin's sense. Whenever A is contractible, the resulting homotopy category of A-algebras (i.e. weak omega-categories) is equivalent to the homotopy category of compactly generated spaces. (C) 2002 Elsevier Science (USA).
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