# Spahn Clemens Berger, A Cellular Nerve for Higher Categories (Rev #2)

## 1. Globular theories and cellular nerves

Contents:

Batanin’s $\omega$-operads are described by their operator categories which are called globular theories.

###### Definition (finite planar level tree)

A finite planar level tree ( or for short just a tree) is a graded set $(T(n))_{n\in \mathhb{N}_0}$ endowed with a map $i_T: T_{\gt 0}$ decreasing the degree by one and such that all fibers $i_T^{-1}(x)$ are linearly ordered.

###### Lemma and Definition ($\omega$-graph of sectors of a tree)

Let $T$ be a tree.

A $T$-sector of height $k$ is defined to be a cospan

$\array{ y^\prime&y^{\prime\prime} \\ \searrow&\swarrow \\ &y }$

Revision on November 18, 2012 at 14:23:00 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.