## A Cellular Nerve for Higher Categories (2002)

by
Clemens Berger

Citations: | 21 - 2 self |

### BibTeX

@MISC{Berger02acellular,

author = {Clemens Berger},

title = {A Cellular Nerve for Higher Categories},

year = {2002}

}

### OpenURL

### Abstract

... categories. 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 YA 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