✦ LIBER ✦

A Cellular Nerve for Higher Categories

✍ Scribed by Clemens Berger

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 481 KB
Volume: 169
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2001.2056

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✦ Synopsis

We realise Joyal's cell category Y as a dense subcategory of the category of ocategories. The associated cellular nerve of an o-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 Y A of the category of % A-algebras for each o-operad A in Batanin's sense. Whenever A is contractible, the resulting homotopy category of % A-algebras (i.e. weak o-categories) is equivalent to the homotopy category of compactly generated spaces. # 2002 Elsevier Science (USA)

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